Shape　memory　polymers　(SMPs)　are　a　novel　class　of　shape　memory　materials　which　can　store　a　deformed　(temporary)　shape　and　recover　an　original　(permanent)　shape　under　a　shape　memory　thermomechanical　loading-unloading　cycle.　The　deformation　mechanisms　of　SMPs　are　very　complicated,　but　the　SMPs　also　have　a　lot　of　advantages　and　the　widespread　application　value　and　prospect.　So　developing　proper　constitutive　models　that　describe　thermomechanical　properties　of　SMPs　and　the　shape　memory　effect　is　very　challenging　and　of　great　theoretical　and　application　value.　Based　on　the　deformation　mechanisms　and　considerable　experimental　investigations　of　SMPs,　researchers　have　developed　many　constitutive　models.　This　article　investigates　the　deformation　mechanism　and　introduces　the　recent　research　advance　of　the　constitutive　models　of　thermal-sensitive　SMPs.　Special　emphases　are　given　on　the　micromechanical　constitutive　relations　in　which　the　deformation　is　considered　being　based　on　the　microstructure　of　the　SMPs.　Finally,　the　lack　of　research　and　prospects　for　further　research　are　discussed.　(C)　2011　Wiley　Periodicals,　Inc.　J　Appl　Polym　Sci　123:　1502-1508,　2012