Magnesium (Mg) has emerged as an ideal alternative to the permanent implant materials owing to its enhanced properties such as biodegradation, better mechanical strengths than polymeric biodegradable materials and biocompatibility. It has been under investigation as an implant material both in cardiovascular and orthopedic applications. The use of Mg as an implant material reduces the risk of long-term incompatible interaction of implant with tissues and eliminates the second surgical procedure to remove the implant, thus minimizes the complications. The hurdle in the extensive use of Mg implants is its fast degradation rate, which consequently reduces the mechanical strength to support the implant site. Alloy development, surface treatment, and design modification of implants are the routes that can lead to the improved corrosion resistance of Mg implants and extensive research is going on in all three directions. In this review, the recent trends in the alloying and surface treatment of Mg have been discussed in detail. Additionally, the recent progress in the use of computational models to analyze Mg bioimplants has been given special consideration.