Urinary incontinence affects more than 300 million people worldwide. The implantation of a medical device called an artificial urinary sphincter (AUS) is the gold standard treatment when conservative and minimally invasive therapies fail. In this article, the AUSs (extra-urethral and endo-urethral sphincters) available on the market, both presented at the research level and filed as patents, are reviewed. The ability of the different solutions to effectively replace the natural sphincter are discussed, together with advantages and some possible side effects, such as tissue atrophy, overall invasiveness of the implant, and so forth. Finally, future research priorities are discussed for both endo-urethral and extra-urethral approaches considering key engineering aspects, such as materials, compression and closure mechanisms, and implantation methods, with the long-term aim of developing an effective, reliable, durable, and minimally invasive AUS capable of restoring a normal quality of life for incontinent patients.