We will discuss two topics. First we will revisit the asymptotic structure of classical de Sitter space. In particular we will construct charges at future infinity (I^+) and obtain the asymptotic symmetry group drawing parallels with the BMS group of flat space. Secondly, move away from the region I^+ and study the space living near the cosmological horizon by considering large rotating Nariai black holes whose size tends to that of the cosmological horizon. We will examine the resulting near (cosmological) horizon geometry and find an interesting asymptotic structure containing the Virasoro algebra, suggestive of a holographic interpretation.