Biocompatible and biodegradable block copolymers (BBCPs) containing crystalline blocks become increasingly important in polymer science, and have great potential applications in polymer materials. Crystallization in polymers is accompanied by the adoption of an extended conformation, or often by chain folding. It is important to distinguish between crystallization in homopolymers and in block copolymers. In homopolymers, chain folding leads to metastable structures introduced by the crystallization kinetics. In contrast, equilibrium chain folding in diblocks can be achieved as the equilibrium number of the folds is controlled by the size of the second block. The structures of BBCPs, which are determined by the competition between crystallization, microphase separation, kinetics and processing, have a tremendous influence on the final properties and applications. In this review, we present the recent advances on crystalline-crystalline diblock copolymer in our group.