A central program in the study of a geometric PDE is to define a notion of generalized solution, and then establish a partial regularity theory to describe the behavior of such a solution near its singularities. Perelman carried out this program for Ricci flow in dimension 3 with his notion of Ricci flow with surgery, but this relied on a classification of all possible singularities. In higher dimensions, where such a classification is impossible, Ricci flow has until recently resisted a general notion of weak solution, in part due to the lack of an ambient space. The goal of this talk is to survey notions of generalized Ricci flow solutions, including Perelman's Ricci flow with surgery, Song-Tian's Kahler-Ricci flow through birational maps, and Bamler's recent breakthroughs related to singular Ricci flow spacetimes.