Biocompatible and biodegradable block copolymers (BBCPs) have become increasingly important in polymer science, and have many potential applications in polymer materials. 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, the most recent advances are highlighted in the crystalline structures and morphologies of BBCPs with at least one crystalline block. Particular emphasis is placed on the influences of chemical composition, molecular architecture, crystallization pathway, and film thickness on the structures and morphologies of the block copolymers. The formation and the characteristics of the structures grown in the block copolymers are helpful for understanding the interplay between crystallization and phase segregation, morphologies, structural evolution and their applications.