Polyurethanes (PUs), formed by the reaction of diisocyanates with polyols (or equivalent) in the presence of a catalyst, have a wide variety of industrial uses. Much recent attention has focused on their biomedical applications, owing to their biocompatibility, biodegradability and tailorable chemical and physical forms. Examples of such application areas include antibacterial surfaces and catheters, drug delivery vehicles, stents, surgical dressings/pressure sensitive adhesives, tissue engineering scaffolds and electrospinning, nerve generation, cardiac patches and PU coatings for breast implants. Following a brief introduction to PUs, this review surveys selected articles, mostly from 2014 to 2017, that highlight this diverse range of biomedical applications offered by PU materials and coatings.