diff --git a/etc/ORG-NEWS b/etc/ORG-NEWS
index c115cf9c1..ec8a0c27a 100644
--- a/etc/ORG-NEWS
+++ b/etc/ORG-NEWS
@@ -86,10 +86,15 @@ Where clue > 0
 
 [[http://plantuml.com/][Plantuml]] source blocks now support the [[http://orgmode.org/manual/prologue.html#prologue][~:prologue~]], [[http://orgmode.org/manual/epilogue.html#epilogue][~:epilogue~]] and
 [[http://orgmode.org/manual/var.html#var][~:var~]] header arguments.
+*** Export
+**** Implement ~org-export-insert-image-links~
+This new function is meant to be used in back-ends supporting images
+as descriptions of links, a.k.a. image links.  See its docstring for
+details.
+**** Horizontal rules are no longer ignored in LaTeX table math mode
 
 *** New variable : ~org-bibtex-headline-format-function~
 This allow to use a different title than entry title.
-*** Horizontal rules are no longer ignored in LaTeX table math mode
 
 ** Removed functions
 
diff --git a/lisp/ox-html.el b/lisp/ox-html.el
index 63a8c847a..eb728dfa1 100644
--- a/lisp/ox-html.el
+++ b/lisp/ox-html.el
@@ -101,6 +101,7 @@
     (verbatim . org-html-verbatim)
     (verse-block . org-html-verse-block))
   :filters-alist '((:filter-options . org-html-infojs-install-script)
+		   (:filter-parse-tree . org-html-image-link-filter)
 		   (:filter-final-output . org-html-final-function))
   :menu-entry
   '(?h "Export to HTML"
@@ -2835,6 +2836,9 @@ CONTENTS is nil.  INFO is a plist holding contextual information."
 
 ;;;; Link
 
+(defun org-html-image-link-filter (data _backend info)
+  (org-export-insert-image-links data info org-html-inline-image-rules))
+
 (defun org-html-inline-image-p (link info)
   "Non-nil when LINK is meant to appear as an image.
 INFO is a plist used as a communication channel.  LINK is an
diff --git a/lisp/ox-latex.el b/lisp/ox-latex.el
index 74969e4c4..9881cd849 100644
--- a/lisp/ox-latex.el
+++ b/lisp/ox-latex.el
@@ -101,7 +101,8 @@
 		(org-open-file (org-latex-export-to-pdf nil s v b)))))))
   :filters-alist '((:filter-options . org-latex-math-block-options-filter)
 		   (:filter-parse-tree org-latex-math-block-tree-filter
-				       org-latex-matrices-tree-filter))
+				       org-latex-matrices-tree-filter
+				       org-latex-image-link-filter))
   :options-alist
   '((:latex-class "LATEX_CLASS" nil org-latex-default-class t)
     (:latex-class-options "LATEX_CLASS_OPTIONS" nil nil t)
@@ -724,7 +725,8 @@ environment."
   :safe #'stringp)
 
 (defcustom org-latex-inline-image-rules
-  '(("file" . "\\.\\(pdf\\|jpeg\\|jpg\\|png\\|ps\\|eps\\|tikz\\|pgf\\|svg\\)\\'"))
+  `(("file" . ,(regexp-opt
+		'("pdf" "jpeg" "jpg" "png" "ps" "eps" "tikz" "pgf" "svg"))))
   "Rules characterizing image files that can be inlined into LaTeX.
 
 A rule consists in an association whose key is the type of link
@@ -2268,6 +2270,9 @@ CONTENTS is nil.  INFO is a plist holding contextual information."
 
 ;;;; Link
 
+(defun org-latex-image-link-filter (data _backend info)
+  (org-export-insert-image-links data info org-latex-inline-image-rules))
+
 (defun org-latex--inline-image (link info)
   "Return LaTeX code for an inline image.
 LINK is the link pointing to the inline image.  INFO is a plist
diff --git a/lisp/ox-odt.el b/lisp/ox-odt.el
index 24658363c..92c54cf8d 100644
--- a/lisp/ox-odt.el
+++ b/lisp/ox-odt.el
@@ -85,7 +85,8 @@
   :filters-alist '((:filter-parse-tree
 		    . (org-odt--translate-latex-fragments
 		       org-odt--translate-description-lists
-		       org-odt--translate-list-tables)))
+		       org-odt--translate-list-tables
+		       org-odt--translate-image-links)))
   :menu-entry
   '(?o "Export to ODT"
        ((?o "As ODT file" org-odt-export-to-odt)
@@ -3687,6 +3688,11 @@ contextual information."
 
 ;;; Filters
 
+;;; Images
+
+(defun org-odt--translate-image-links (data _backend info)
+  (org-export-insert-image-links data info inline image rules))
+
 ;;;; LaTeX fragments
 
 (defun org-odt--translate-latex-fragments (tree _backend info)
diff --git a/lisp/ox.el b/lisp/ox.el
index 4adfd743e..5e361792f 100644
--- a/lisp/ox.el
+++ b/lisp/ox.el
@@ -4160,12 +4160,55 @@ the provided rules is non-nil.  The default rule is
 This only applies to links without a description."
   (and (not (org-element-contents link))
        (let ((case-fold-search t))
-	 (catch 'exit
-	   (dolist (rule (or rules org-export-default-inline-image-rule))
-	     (and (string= (org-element-property :type link) (car rule))
-		  (string-match-p (cdr rule)
-				  (org-element-property :path link))
-		  (throw 'exit t)))))))
+	 (cl-some (lambda (rule)
+		    (and (string= (org-element-property :type link) (car rule))
+			 (string-match-p (cdr rule)
+					 (org-element-property :path link))))
+		  (or rules org-export-default-inline-image-rule)))))
+
+(defun org-export-insert-image-links (data info &optional rules)
+  "Insert image links in DATA.
+
+Org syntax do not support nested links.  Nevertheless, some
+export back-ends support image as descriptions of links.  Since
+images are really link to image files, we need to make an
+exception about link nesting.
+
+This function recognizes links whose contents are really images
+and turn them into proper nested links.  It is meant to be used
+as a parse tree filter in back-ends supporting such constructs.
+
+DATA is a parse tree.  INFO is the current state of the export
+process, as a plist.
+
+A description is a valid images if it matches any rule in RULES,
+if non-nil, or `org-export-default-inline-image-rule' otherwise.
+See `org-export-inline-image-p' for more information about the
+structure of RULES.
+
+Return modified DATA."
+  (let ((link-re (format "\\`\\(?:%s\\|%s\\)\\'"
+			 org-plain-link-re
+			 org-angle-link-re))
+	(case-fold-search t))
+    (org-element-map data 'link
+      (lambda (l)
+	(let ((contents (org-element-interpret-data (org-element-contents l))))
+	  (when (and (org-string-nw-p contents)
+		     (string-match link-re contents))
+	    (let ((type (match-string 1 contents))
+		  (path (match-string 2 contents)))
+	      (when (cl-some (lambda (rule)
+			       (and (string= type (car rule))
+				    (string-match-p (cdr rule) path)))
+			     (or rules org-export-default-inline-image-rule))
+		(org-element-set-contents
+		 l
+		 (with-temp-buffer
+		   (save-excursion (insert contents))
+		   (org-element-link-parser))))))))
+      info nil nil t))
+  data)
 
 (defun org-export-resolve-coderef (ref info)
   "Resolve a code reference REF.