This article explores several extensions of the Prüfer domain notion to rings with zero divisors. These extensions include semihereditary rings, rings with weak global dimension less than or equal to 1, arithmetical rings, Gaussian rings, locally Prüfer rings, strongly Prüfer rings, and Prüfer rings. The renewed interest in these properties, due to their connection to Kaplansky’s Conjecture, has resulted in a large body of results shedding new light on the area. We survey the work done in this direction in the last 15years, including results, examples and counterexamples, and a multitude of open problems. KeywordsSemihereditary ring–Ring with global weak dimension at most 1–Arithmetical ring–Gaussian ring–Prüfer ring