Elliptic de Sitter space (edS) is a maximally symmetric spacetime with an unusual global topology: there is no global distinction between past and future. I will describe the spacetime in detail and indicate why it is a natural background for physics. For example, an observer in edS has complete information despite the presence of horizons. I will also outline the construction of edS in a variant of string theory, and mention some peculiar aspects of the holographic dual theory.