diff --git a/accessible/base/AccIterator.h b/accessible/base/AccIterator.h
index 15c3aaf688e7..f24ea1f54876 100644
--- a/accessible/base/AccIterator.h
+++ b/accessible/base/AccIterator.h
@@ -279,7 +279,7 @@ private:
 class ItemIterator : public AccIterable
 {
 public:
-  explicit ItemIterator(Accessible* aItemContainer) :
+  explicit ItemIterator(const Accessible* aItemContainer) :
     mContainer(aItemContainer), mAnchor(nullptr) { }
   virtual ~ItemIterator() { }
 
@@ -290,7 +290,7 @@ private:
   ItemIterator(const ItemIterator&) = delete;
   ItemIterator& operator = (const ItemIterator&) = delete;
 
-  Accessible* mContainer;
+  const Accessible* mContainer;
   Accessible* mAnchor;
 };
 
diff --git a/accessible/generic/Accessible.cpp b/accessible/generic/Accessible.cpp
index d2ecee7f0643..226abd094595 100644
--- a/accessible/generic/Accessible.cpp
+++ b/accessible/generic/Accessible.cpp
@@ -1627,7 +1627,7 @@ Accessible::GetAtomicRegion() const
 }
 
 Relation
-Accessible::RelationByType(RelationType aType)
+Accessible::RelationByType(RelationType aType) const
 {
   if (!HasOwnContent())
     return Relation();
@@ -2733,7 +2733,7 @@ Accessible::GetActionRule() const
 }
 
 AccGroupInfo*
-Accessible::GetGroupInfo()
+Accessible::GetGroupInfo() const
 {
   if (IsProxy())
     MOZ_CRASH("This should never be called on proxy wrappers");
diff --git a/accessible/generic/Accessible.h b/accessible/generic/Accessible.h
index 0c7df72b2150..df79dca60837 100644
--- a/accessible/generic/Accessible.h
+++ b/accessible/generic/Accessible.h
@@ -367,7 +367,7 @@ public:
   /**
    * Get the relation of the given type.
    */
-  virtual Relation RelationByType(RelationType aType);
+  virtual Relation RelationByType(RelationType aType) const;
 
   //////////////////////////////////////////////////////////////////////////////
   // Initializing methods
@@ -1131,7 +1131,7 @@ protected:
   /**
    * Return group info.
    */
-  AccGroupInfo* GetGroupInfo();
+  AccGroupInfo* GetGroupInfo() const;
 
   // Data Members
   nsCOMPtr<nsIContent> mContent;
@@ -1155,7 +1155,7 @@ protected:
   /**
    * Keep in sync with StateFlags, ContextFlags, and AccTypes.
    */
-  uint32_t mStateFlags : kStateFlagsBits;
+  mutable uint32_t mStateFlags : kStateFlagsBits;
   uint32_t mContextFlags : kContextFlagsBits;
   uint32_t mType : kTypeBits;
   uint32_t mGenericTypes : kGenericTypesBits;
@@ -1187,7 +1187,7 @@ protected:
   {
     AccGroupInfo* groupInfo;
     ProxyAccessible* proxy;
-  } mBits;
+  } mutable mBits;
   friend class AccGroupInfo;
 
 private:
diff --git a/accessible/generic/ApplicationAccessible.cpp b/accessible/generic/ApplicationAccessible.cpp
index fc40ae72ca6d..e7ae61bd4375 100644
--- a/accessible/generic/ApplicationAccessible.cpp
+++ b/accessible/generic/ApplicationAccessible.cpp
@@ -110,7 +110,7 @@ ApplicationAccessible::FocusedChild()
 }
 
 Relation
-ApplicationAccessible::RelationByType(RelationType aRelationType)
+ApplicationAccessible::RelationByType(RelationType aRelationType) const
 {
   return Relation();
 }
diff --git a/accessible/generic/ApplicationAccessible.h b/accessible/generic/ApplicationAccessible.h
index b621304cff39..cf9311c55b0e 100644
--- a/accessible/generic/ApplicationAccessible.h
+++ b/accessible/generic/ApplicationAccessible.h
@@ -47,7 +47,7 @@ public:
   virtual mozilla::a11y::role NativeRole() const override;
   virtual uint64_t State() override;
   virtual uint64_t NativeState() override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   virtual Accessible* ChildAtPoint(int32_t aX, int32_t aY,
                                    EWhichChildAtPoint aWhichChild) override;
diff --git a/accessible/generic/HyperTextAccessible.cpp b/accessible/generic/HyperTextAccessible.cpp
index 06430ce84663..9b48b974a59e 100644
--- a/accessible/generic/HyperTextAccessible.cpp
+++ b/accessible/generic/HyperTextAccessible.cpp
@@ -1922,7 +1922,7 @@ HyperTextAccessible::InsertChildAt(uint32_t aIndex, Accessible* aChild)
 }
 
 Relation
-HyperTextAccessible::RelationByType(RelationType aType)
+HyperTextAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = Accessible::RelationByType(aType);
 
diff --git a/accessible/generic/HyperTextAccessible.h b/accessible/generic/HyperTextAccessible.h
index 63221e66655e..0dc500e3d290 100644
--- a/accessible/generic/HyperTextAccessible.h
+++ b/accessible/generic/HyperTextAccessible.h
@@ -63,7 +63,7 @@ public:
   virtual void Shutdown() override;
   virtual bool RemoveChild(Accessible* aAccessible) override;
   virtual bool InsertChildAt(uint32_t aIndex, Accessible* aChild) override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   // HyperTextAccessible (static helper method)
 
diff --git a/accessible/generic/RootAccessible.cpp b/accessible/generic/RootAccessible.cpp
index 844c22f5d540..0df84abd9a4c 100644
--- a/accessible/generic/RootAccessible.cpp
+++ b/accessible/generic/RootAccessible.cpp
@@ -480,7 +480,7 @@ RootAccessible::Shutdown()
 }
 
 Relation
-RootAccessible::RelationByType(RelationType aType)
+RootAccessible::RelationByType(RelationType aType) const
 {
   if (!mDocumentNode || aType != RelationType::EMBEDS)
     return DocAccessibleWrap::RelationByType(aType);
diff --git a/accessible/generic/RootAccessible.h b/accessible/generic/RootAccessible.h
index cb1bf4145920..6452d85ca8a3 100644
--- a/accessible/generic/RootAccessible.h
+++ b/accessible/generic/RootAccessible.h
@@ -30,7 +30,7 @@ public:
   // Accessible
   virtual void Shutdown() override;
   virtual mozilla::a11y::ENameValueFlag Name(nsString& aName) override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
   virtual mozilla::a11y::role NativeRole() const override;
   virtual uint64_t NativeState() override;
 
diff --git a/accessible/html/HTMLElementAccessibles.cpp b/accessible/html/HTMLElementAccessibles.cpp
index 5bb38f26ebbe..e0cb7d43a3be 100644
--- a/accessible/html/HTMLElementAccessibles.cpp
+++ b/accessible/html/HTMLElementAccessibles.cpp
@@ -64,7 +64,7 @@ HTMLLabelAccessible::NativeName(nsString& aName)
 }
 
 Relation
-HTMLLabelAccessible::RelationByType(RelationType aType)
+HTMLLabelAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType == RelationType::LABEL_FOR) {
@@ -106,7 +106,7 @@ HTMLLabelAccessible::DoAction(uint8_t aIndex)
 ////////////////////////////////////////////////////////////////////////////////
 
 Relation
-HTMLOutputAccessible::RelationByType(RelationType aType)
+HTMLOutputAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType == RelationType::CONTROLLED_BY)
diff --git a/accessible/html/HTMLElementAccessibles.h b/accessible/html/HTMLElementAccessibles.h
index 9eb8939b8319..bd32bb91b66e 100644
--- a/accessible/html/HTMLElementAccessibles.h
+++ b/accessible/html/HTMLElementAccessibles.h
@@ -61,7 +61,7 @@ public:
                                        HyperTextAccessibleWrap)
 
   // Accessible
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   // ActionAccessible
   virtual uint8_t ActionCount() override;
@@ -87,7 +87,7 @@ public:
                                        HyperTextAccessibleWrap)
 
   // Accessible
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
 protected:
   virtual ~HTMLOutputAccessible() {}
diff --git a/accessible/html/HTMLFormControlAccessible.cpp b/accessible/html/HTMLFormControlAccessible.cpp
index 050b9487f159..e35e5b98e4ad 100644
--- a/accessible/html/HTMLFormControlAccessible.cpp
+++ b/accessible/html/HTMLFormControlAccessible.cpp
@@ -734,7 +734,7 @@ HTMLGroupboxAccessible::NativeName(nsString& aName)
 }
 
 Relation
-HTMLGroupboxAccessible::RelationByType(RelationType aType)
+HTMLGroupboxAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessibleWrap::RelationByType(aType);
     // No override for label, so use <legend> for this <fieldset>
@@ -755,7 +755,7 @@ HTMLLegendAccessible::
 }
 
 Relation
-HTMLLegendAccessible::RelationByType(RelationType aType)
+HTMLLegendAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessibleWrap::RelationByType(aType);
   if (aType != RelationType::LABEL_FOR)
@@ -793,7 +793,7 @@ HTMLFigureAccessible::NativeName(nsString& aName)
 }
 
 Relation
-HTMLFigureAccessible::RelationByType(RelationType aType)
+HTMLFigureAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessibleWrap::RelationByType(aType);
   if (aType == RelationType::LABELLED_BY)
@@ -827,7 +827,7 @@ HTMLFigcaptionAccessible::
 }
 
 Relation
-HTMLFigcaptionAccessible::RelationByType(RelationType aType)
+HTMLFigcaptionAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessibleWrap::RelationByType(aType);
   if (aType != RelationType::LABEL_FOR)
diff --git a/accessible/html/HTMLFormControlAccessible.h b/accessible/html/HTMLFormControlAccessible.h
index 4949d9489adc..0009a5e69cc2 100644
--- a/accessible/html/HTMLFormControlAccessible.h
+++ b/accessible/html/HTMLFormControlAccessible.h
@@ -225,7 +225,7 @@ public:
 
   // Accessible
   virtual mozilla::a11y::role NativeRole() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
 protected:
   // Accessible
@@ -245,7 +245,7 @@ public:
   HTMLLegendAccessible(nsIContent* aContent, DocAccessible* aDoc);
 
   // Accessible
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 };
 
 /**
@@ -257,7 +257,7 @@ public:
   HTMLFigureAccessible(nsIContent* aContent, DocAccessible* aDoc);
 
   // Accessible
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
 protected:
   // Accessible
@@ -277,7 +277,7 @@ public:
   HTMLFigcaptionAccessible(nsIContent* aContent, DocAccessible* aDoc);
 
   // Accessible
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 };
 
 } // namespace a11y
diff --git a/accessible/html/HTMLTableAccessible.cpp b/accessible/html/HTMLTableAccessible.cpp
index 0a2fc53df544..af476117e58e 100644
--- a/accessible/html/HTMLTableAccessible.cpp
+++ b/accessible/html/HTMLTableAccessible.cpp
@@ -455,7 +455,7 @@ HTMLTableAccessible::NativeAttributes()
 // HTMLTableAccessible: Accessible
 
 Relation
-HTMLTableAccessible::RelationByType(RelationType aType)
+HTMLTableAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType == RelationType::LABELLED_BY)
@@ -1104,7 +1104,7 @@ HTMLTableAccessible::IsProbablyLayoutTable()
 ////////////////////////////////////////////////////////////////////////////////
 
 Relation
-HTMLCaptionAccessible::RelationByType(RelationType aType)
+HTMLCaptionAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessible::RelationByType(aType);
   if (aType == RelationType::LABEL_FOR)
diff --git a/accessible/html/HTMLTableAccessible.h b/accessible/html/HTMLTableAccessible.h
index d366889e38d7..e6947dfe825a 100644
--- a/accessible/html/HTMLTableAccessible.h
+++ b/accessible/html/HTMLTableAccessible.h
@@ -165,7 +165,7 @@ public:
   virtual a11y::role NativeRole() const override;
   virtual uint64_t NativeState() override;
   virtual already_AddRefed<nsIPersistentProperties> NativeAttributes() override;
-  virtual Relation RelationByType(RelationType aRelationType) override;
+  virtual Relation RelationByType(RelationType aRelationType) const override;
 
   virtual bool InsertChildAt(uint32_t aIndex, Accessible* aChild) override;
 
@@ -224,7 +224,7 @@ public:
 
   // Accessible
   virtual a11y::role NativeRole() const override;
-  virtual Relation RelationByType(RelationType aRelationType) override;
+  virtual Relation RelationByType(RelationType aRelationType) const override;
 
 protected:
   virtual ~HTMLCaptionAccessible() { }
diff --git a/accessible/xul/XULElementAccessibles.cpp b/accessible/xul/XULElementAccessibles.cpp
index a6832344ad32..0812f19fe53a 100644
--- a/accessible/xul/XULElementAccessibles.cpp
+++ b/accessible/xul/XULElementAccessibles.cpp
@@ -87,7 +87,7 @@ XULLabelAccessible::NativeState()
 }
 
 Relation
-XULLabelAccessible::RelationByType(RelationType aType)
+XULLabelAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = HyperTextAccessibleWrap::RelationByType(aType);
   if (aType == RelationType::LABEL_FOR) {
diff --git a/accessible/xul/XULElementAccessibles.h b/accessible/xul/XULElementAccessibles.h
index 32780ac36574..9fb367973696 100644
--- a/accessible/xul/XULElementAccessibles.h
+++ b/accessible/xul/XULElementAccessibles.h
@@ -26,7 +26,7 @@ public:
   virtual void Shutdown() override;
   virtual a11y::role NativeRole() const override;
   virtual uint64_t NativeState() override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   void UpdateLabelValue(const nsString& aValue);
 
diff --git a/accessible/xul/XULFormControlAccessible.cpp b/accessible/xul/XULFormControlAccessible.cpp
index 6ebe2bca1a9b..b535a77364c5 100644
--- a/accessible/xul/XULFormControlAccessible.cpp
+++ b/accessible/xul/XULFormControlAccessible.cpp
@@ -370,7 +370,7 @@ XULGroupboxAccessible::NativeName(nsString& aName)
 }
 
 Relation
-XULGroupboxAccessible::RelationByType(RelationType aType)
+XULGroupboxAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType != RelationType::LABELLED_BY)
diff --git a/accessible/xul/XULFormControlAccessible.h b/accessible/xul/XULFormControlAccessible.h
index d71a6c288979..ed0281d25dc1 100644
--- a/accessible/xul/XULFormControlAccessible.h
+++ b/accessible/xul/XULFormControlAccessible.h
@@ -111,7 +111,7 @@ public:
 
   // Accessible
   virtual mozilla::a11y::role NativeRole() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
 protected:
   // Accessible
diff --git a/accessible/xul/XULTabAccessible.cpp b/accessible/xul/XULTabAccessible.cpp
index 2473593bc227..c7cd06cf8caf 100644
--- a/accessible/xul/XULTabAccessible.cpp
+++ b/accessible/xul/XULTabAccessible.cpp
@@ -102,7 +102,7 @@ XULTabAccessible::NativeInteractiveState() const
 }
 
 Relation
-XULTabAccessible::RelationByType(RelationType aType)
+XULTabAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType != RelationType::LABEL_FOR)
@@ -189,7 +189,7 @@ XULTabpanelAccessible::NativeRole() const
 }
 
 Relation
-XULTabpanelAccessible::RelationByType(RelationType aType)
+XULTabpanelAccessible::RelationByType(RelationType aType) const
 {
   Relation rel = AccessibleWrap::RelationByType(aType);
   if (aType != RelationType::LABELLED_BY)
diff --git a/accessible/xul/XULTabAccessible.h b/accessible/xul/XULTabAccessible.h
index f26ebbf7e01b..dab939149a16 100644
--- a/accessible/xul/XULTabAccessible.h
+++ b/accessible/xul/XULTabAccessible.h
@@ -28,7 +28,7 @@ public:
   virtual a11y::role NativeRole() const override;
   virtual uint64_t NativeState() override;
   virtual uint64_t NativeInteractiveState() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   // ActionAccessible
   virtual uint8_t ActionCount() override;
@@ -87,7 +87,7 @@ public:
 
   // Accessible
   virtual a11y::role NativeRole() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 };
 
 } // namespace a11y
diff --git a/accessible/xul/XULTreeAccessible.cpp b/accessible/xul/XULTreeAccessible.cpp
index f0ec45aa958d..74d2ced280b3 100644
--- a/accessible/xul/XULTreeAccessible.cpp
+++ b/accessible/xul/XULTreeAccessible.cpp
@@ -433,7 +433,7 @@ XULTreeAccessible::ChildCount() const
 }
 
 Relation
-XULTreeAccessible::RelationByType(RelationType aType)
+XULTreeAccessible::RelationByType(RelationType aType) const
 {
   if (aType == RelationType::NODE_PARENT_OF) {
     if (mTreeView)
@@ -790,7 +790,7 @@ XULTreeItemAccessibleBase::TakeFocus()
 }
 
 Relation
-XULTreeItemAccessibleBase::RelationByType(RelationType aType)
+XULTreeItemAccessibleBase::RelationByType(RelationType aType) const
 {
 
   switch (aType) {
diff --git a/accessible/xul/XULTreeAccessible.h b/accessible/xul/XULTreeAccessible.h
index dd3d94c4c002..53dd53288fd3 100644
--- a/accessible/xul/XULTreeAccessible.h
+++ b/accessible/xul/XULTreeAccessible.h
@@ -48,7 +48,7 @@ public:
 
   virtual Accessible* GetChildAt(uint32_t aIndex) const override;
   virtual uint32_t ChildCount() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
 
   // SelectAccessible
   virtual void SelectedItems(nsTArray<Accessible*>* aItems) override;
@@ -152,7 +152,7 @@ public:
   virtual uint64_t NativeState() override;
   virtual uint64_t NativeInteractiveState() const override;
   virtual int32_t IndexInParent() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
   virtual Accessible* FocusedChild() override;
   virtual void SetSelected(bool aSelect) override;
   virtual void TakeFocus() override;
diff --git a/accessible/xul/XULTreeGridAccessible.cpp b/accessible/xul/XULTreeGridAccessible.cpp
index 72893017b93d..2838211aad31 100644
--- a/accessible/xul/XULTreeGridAccessible.cpp
+++ b/accessible/xul/XULTreeGridAccessible.cpp
@@ -732,7 +732,7 @@ XULTreeGridCellAccessible::IndexInParent() const
 }
 
 Relation
-XULTreeGridCellAccessible::RelationByType(RelationType aType)
+XULTreeGridCellAccessible::RelationByType(RelationType aType) const
 {
   return Relation();
 }
diff --git a/accessible/xul/XULTreeGridAccessible.h b/accessible/xul/XULTreeGridAccessible.h
index cd1c424c97d5..0702fdfc92ab 100644
--- a/accessible/xul/XULTreeGridAccessible.h
+++ b/accessible/xul/XULTreeGridAccessible.h
@@ -132,7 +132,7 @@ public:
   virtual Accessible* FocusedChild() override;
   virtual already_AddRefed<nsIPersistentProperties> NativeAttributes() override;
   virtual int32_t IndexInParent() const override;
-  virtual Relation RelationByType(RelationType aType) override;
+  virtual Relation RelationByType(RelationType aType) const override;
   virtual a11y::role NativeRole() const override;
   virtual uint64_t NativeState() override;
   virtual uint64_t NativeInteractiveState() const override;