  This paper has two parts. First we review the description of local bulk
operators in Lorentzian AdS in terms of non-local operators in the boundary
CFT. We discuss how bulk locality arises in pure AdS backgrounds and how it is
modified at finite N. Next we present some new results on BTZ black holes:
local operators can be defined inside the horizon of a finite N BTZ black hole,
in a way that suggests the BTZ geometry describes an average over black hole
microstates, but with finite N effects resolving the singularity.
