Block copolymers show interesting phase behavior if at least one of the constituting blocks is crystallizable. The morphology development becomes highly complex when such a block copolymer is crystallized above the glass transition temperature of the amorphous block due to competition between microphase separation and crystallization during the structure evolution process. In this review, we focus on the morphology development in such crystalline‐amorphous (C‐A) diblock copolymers where the amorphous block remains rubbery during the crystallization process. Crystallization behavior in bulk as well as in thin films is considered. The issue of crystal orientation and chain folding upon crystallization in these diblock copolymers has been discussed. Moreover, the nucleation mechanism in these C‐A diblock copolymers and its effect on their crystallization kinetics is also described. Some of the emerging areas of research such as crystallization behavior in blend of C‐A diblock copolymers has been briefly discussed and finally the future challenges, which holds promise for our further in‐depth understanding of crystallization in block copolymers, has been identified.