  We discuss the logic of, and some puzzles in, the various approaches to
thermodynamics of gravitational systems. In particular the blackhole, deSitter
(dS), black hole in dS (SdS) and in Anti-deSitter SAdS backgrounds are
considered. After reviewing the original calculations of Hawking and Gibbons we
discuss an alternative Hamiltonian method. This justifies the lowest order
Euclidean calculation but is free of the problems associated with the latter
when going to higher orders. To conclude we address the sign issue in dS
thermodynamics.
