Enriques surfaces are special free quotients of K3 surfaces by a fixed point free involution. In higher dimension the notion can be generalized and one can introduce Enriques manifolds and in the singular setting, Log Enriques vaieties. In this talk I will explain general properties of Enriques manifolds and of Log Enriques varieties. I will then provide and discuss several examples in the singular setting, in particular  I will talk about Log Enriques varieties that arise as quotients of generalized Fermat manifolds. These manifolds were studied recently by Hidalgo, Hughes and Leyton-Alvarez. 
The results that I will present are contained in several joint papers with S. Boissière, C. Camere, M. Nieper-Wisskirchen and in a recent work in progress with A. Palomino.