Pelvic organ prolapse (POP) is an abnormality of the female pelvic anatomy due to events, such as multiple child births, menopause, and morbid obesity, which may lead to weakening of the pelvic floor striated muscles and smooth musculo-connective tissues. POP leads to dropping of the pelvic organs, namely, the bladder, uterus, and rectum into the vaginal canal and eventual protrusion, causing vaginal pain, pressure, difficulty emptying the bladder and rectum, and sexual dysfunction. Each year, close to 300,000 POP surgeries are performed in the U.S., out of which more than 60% of patients may face relapse conditions. A closer look into the problem reveals that POP surgery failures may be attributed mainly to the lack of understanding among medical practitioners on the mechanics of prolapse. In the literature, there have been attempts in the engineering community to understand prolapse using phenomenological computational modeling. This paper reviews the development and study of these numerical models, aimed at understanding the mechanics of POP. The various computational challenges related to geometry creation, material modeling, finite-element (FE) modeling, and boundary conditions (BCs) will be discussed and significant future research directions will also be highlighted in this review.