Abstract: In this talk, which is based on joint work with Denisi, Ortiz and Xie, I will introduce the class of primitive Enriques varieties. I will discuss the basic properties of these objects, showing in particular that the smooth ones are Enriques manifolds, and I will also present some examples of (singular) primitive Enriques varieties. Finally, I will sketch the proof of the following termination statement: if X is an Enriques manifold and B is an R-divisor on X such that the pair (X,B) is log canonical, then any (K_X+B)-MMP terminates.