Until now there has been no fundamental theory applicable for biodegradable metals (BMs). First, this paper optimizes the definition of BMs given in 2014. Second, the dual criteria of biodegradability and biocompatibility are proposed for BMs, and all metallic elements in the periodic table with accessible data are screened on the basis of these criteria. Regarding biodegradability, electrode potential, reactivity series, galvanic series, Pilling–Bedworth ratio, and Pourbaix diagrams are all adopted as parameters to classify the degradable and nondegradable nature of a material, especially in a physiological environment. Considering the biocompatibility at different levels, cellular biocompatibility, tissue biocompatibility, and human/clinical related biocompatibility parameters are put forward to comprehensively evaluate the biosafety of BMs. Third, for the material design of BMs, mechanical properties, chemical properties, physical properties and biological properties should be considered and balanced to guarantee that the degradation behavior of BMs match well with a tissue regeneration/repair procedure as the function of time and spatial location. Besides the selected metallic elements, some nonmetallic elements are selected as suitable alloying elements for BMs. Finally, five classification/research directions for future BMs are proposed: biodegradable pure metals, crystalline alloys, bulk metallic glasses, high entropy alloys, and metal matrix composites.