Sutures that biodegrade and dissolve over a period of several weeks are in great demand to stitch wounds and surgical incisions. These new materials are receiving increased acceptance across surgical procedures whenever permanent sutures and long-term care are not needed. Unfortunately, both inflammatory responses and adverse local tissue reactions in the close-to-stitching environment are often reported for biodegradable polymeric sutures currently used by the medical community. While bioabsorbable metals are predominantly investigated and tested for vascular stent or osteosynthesis applications, they also appear to possess adequate bio-compatibility, mechanical properties, and corrosion stability to replace biodegradable polymeric sutures. In this Review, biodegradable alloys made of iron, magnesium, and zinc are critically evaluated as potential materials for the manufacturing of soft and hard tissue sutures. In the case of soft tissue closing and stitching, these metals have to compete against currently available degradable polymers. In the case of hard tissue closing and stitching, biodegradable sternal wires could replace the permanent sutures made of stainless steel or titanium alloys. This Review discusses the specific materials and degradation properties required by all suture materials, summarizes current suture testing protocols and provides a well-grounded direction for the potential future development of biodegradable metal based sutures.