The present study deals with thermally induced one-way and invertible two-way shape-memory effect (SME) in covalent networks on the basis of crystallizable (co)polymers and their blends and is an attempt to generalize the results of own investigation received by the authors in the last ten years. The main focus of work clearly lies on research of covalently crosslinked binary and ternary blends having two and three crystalline phases with different thermal stability, respectively. The existence of two or three crystalline phases possessing different melting and crystallization temperatures in heterogeneous polymer networks can lead to triple-shape or even quadruple-shape behavior of such networks. However, the performed investigations point to crucial effect of phase morphology of crosslinked polymer blends on multiplicity of their shapememory behavior beside the influence of blend content, crystallinity and cross-link density of blend phases as well as of processing conditions. For instance, triple-shape memory behavior in binary blends can be realized only if the continuous phase has a lower melting temperature than the dispersed phase. Cross-linked polymer blends are a facile alternative to expensive and complex synthesis of interpenetrating or block-copolymer networks used for shape memory polymers. In addition to findings of experimental investigation of SME in crystallizable covalent polymer networks, the results of modeling their shape-memory behavior on the basis of self-developed physically reasonable model have been briefly described and discussed. Thereby, good accordance between results of theory and experiment was achieved with physically justified fitting parameters