The most popular treatment/management modality for coronary artery disease, which is one of the leading causes of death, is percutaneous transluminal coronary intervention (popularly known as "plain old balloon angioplasty") followed by implantation of a stent ("stenting"). Stent types have evolved from bare metal stents through first-generation drug-eluting stents to fully bioresorbable stents (FBRSs). Two examples of FBRSs are 1) Mg scaffold with no coating; and 2) Mg alloy scaffold coated with a bioresorbable polymer in which an anti-proliferative drug is embedded. In the case of Mg/Mg alloy FBRSs, one of the reported clinical results is that the resorption time of the stent is too short (<∼4 mo to ∼12 mo), a consequence of the high corrosion rate of the metal/alloy. The present review article contains 1) a summarized but comprehensive comparison and contrast of all the types of stents, with special reference to Mg/Mg alloy FBRSs; 2) a critical review of the body of literature on methods to reduce the corrosion rate of Mg/Mg alloy specimens in various aqueous biosimulating media that may have implications for plain Mg/Mg alloy FBRSs, examples of such methods being alloy chemistry modification and fabrication using a nanocomposite; and 3) directions for future work on Mg/Mg alloy FBRSs that draw upon the findings highlighted in item (2) above as well as on other ideas, such as utilization of a Mg matrix composite and fabrication using a metal additive manufacturing method. Thus, information given in this review may find use in work on decreasing the in vivo resorption time (and, hence, improving the clinical efficacy) of the current generation of fully-bioresorbable Mg/Mg-alloy stents as well as guide the development of the next generation of these stents.