During　the　past　two　decades,　the　search　of　strategies　to　introduce　polyoxometalate　(POM)　clusters　as　secondary　building　units　(SBUs)　to　construct　porous　extended　POM-organic　frameworks　(POMOFs)　and　discrete　POM-organic　polyhedra　(POMOPs)　have　attracted　sustained　interests　because　such　materials　not　only　integrate　the　advantages　of　both　POMs　and　framework/polyhedra　structures,　but　also　exhibit　good　prospects　in　photo-/electro-catalysis,　separation,　molecular　recognition,　host-guest　chemistry　and　so　on.　In　this　review,　the　recent　advancements　of　POMOFs　and　POMOPs,　including　their　assembly　methodologies,　classification　and　related　applications　are　summarized.　Moreover,　the　current　challenges　in　the　design　and　fabrication　of　POMOFs　and　POMOPs　as　well　as　the　great　potential　in　these　two　areas　are　also　discussed.　(C)　2019　Elsevier　B.V.　All　rights　reserved.