Abstract This review discusses the current state and challenges in understanding Mg alloy corrosion behavior, in view of use of these materials for biodegradable implants. After the description of some basic and specific aspects of Mg alloy corrosion, the influence of specific biological environments on the corrosion behavior of Mg alloys is summarized. Interactions between corroding Mg surfaces and cells are shortly discussed. Moreover, approaches to control the corrosion and biological performance of Mg alloys by surface modification are presented. The article tries to provide general, instead of alloy specific, information on the topics covered.