Let D be an integral domain and t be the so-called t-operation on D. Then D is a PvMD if and only if \(D_P\) is a valuation domain for all maximal t-ideals P of D. The notion of PvMDs is a very natural generalization of Prüfer domains; in fact, a Prüfer domain is just a PvMD whose nonzero maximal ideals are t-ideals. In this survey article, we study some basic ring-theoretic properties of PvMDs with focus on polynomial rings, Nagata rings, a special type of rings between these two rings, rings of Krull type, and two generalizations of PvMDs. We also deal with the question of when the rings \(A+XB[X]\) and D[[X]] are PvMDs. Finally, we review some results characterizing the PvMD in terms of w-analogs of flat modules, projective modules, injective modules, and so on.