Abstract: In this talk, we aim to address the question: What is the higher-dimensional analogue of Enriques surfaces? We will introduce the class of Enriques varieties and outline their fundamental properties, including stability under the minimal model program and the termination of flips. Additionally, we will present several illustrative examples of Enriques varieties. Joint ongoing work with F. Denisi, N. Tsakanikas and Z. Xie