This talk explores the sign problem in lattice calculations. For concreteness, the talk focuses on the energy density as a function of theta for gauge theories when a topological CP violating term is included.
The emphasis is on subtleties associated with the the infinite volume limit.  A key question addressed is the extent to which information about the infinite volume limit of the energy density as a function of
topological charge density is sufficient to fully reconstruct the infinite volume energy density as a function of theta. Implications for more general problems in QCD where sign problems arise will be discussed.