In　recent　years,　the　technologies　related　to　3D-synthesized　images,　such　as　free　viewpoint　video　and　3D　television,　have　attracted　considerable　attention　due　to　their　extensive　applications　in　fields　like　distance　education,　entertainment,　and　remote　monitoring.　The　new　viewpoints　generated　by　the　depth　image-based　rendering　(DIBR)　technique　are　synthesized　in　reference-free　image　environments　(in　“blind”　environments),　so　there　is　an　urgent　need　for　no-reference　quality　assessment　(QA)　methods　of　3D-synthesized　images.　However,　most　traditional　no-reference　QA　models　fail　to　effectively　measure　the　geometric　distortions　caused　by　DIBR.　For　the　3D-synthesized　image　QA,　this　chapter　first　introduces　the　no-reference　QA　methods　on　the　basis　of　autoregressive　modeling　and　multi-scale　natural　scene　statistical　analysis　to　measure　geometric　distortion.　Second,　it　describes　the　no-reference　QA　methods　on　the　basis　of　pixel-based　changes　in　transform　domains　to　capture　color　and　depth　distortion.　Third,　it　presents　no-reference　QA　methods　based　on　the　structural　variations　caused　by　geometric,　sharpness,　and　color　distortions　to　evaluate　the　blurred,　discontinuous,　and　stretched　3D-synthesized　image　quality.　Finally,　the　above-mentioned　QA　methods　are　validated　on　relevant　databases,　and　the　necessity　of　proposing　efficient　3D-synthesized　image　QA　methods　is　pointed　out.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.