Biodegradable polymer is playing an increasingly significant role in the development of biomedical materials due to its good biocompatibility and biodegradability, and is undoubtedly the focus in the biomedical fields, such as controlled drug delivery, tissue engineering, and regenerative medicine. In this review, some new degradable biomedical copolymers reported over the past 5 years are introduced and discussed in combination with some our research results. The molecular design, chemical structures and related properties of these novel biodegradable copolymers are reported. In summarizing the review, the development, potential applications and future directions of the degradable biomedical copolymers are discussed.