Magnesium-based alloys exhibit biodegradable, biocompatible and excellent mechanical properties which enable them to serve as ideal candidate biomedical materials. In particular, their biodegradable ability helps patients to avoid a second surgery. The corrosion rate, however, is too rapid to sustain the healing process. Alloying is an effective method to slow down the corrosion rate. However, currently magnesium alloys used as biomaterials are mostly commercial alloys without considering cytotoxicity from the perspective of biosafety. This article comprehensively reviews the status of various existing and newly developed degradable magnesium-based alloys specially designed for biomedical application. The effects of critical alloying elements, compositions, heat treatment and processing technology on the microstructure, mechanical properties and corrosion resistance of magnesium alloys are discussed in detail. This article covers Mg-Ca based, Mg-Zn based, Mg-Sr based, Mg-RE based and Mg-Cu-based alloy systems. The novel methods of fabricating Mg-based biomaterials and surface treatment on Mg based alloys for potential biomedical applications are summarized.