  We develop the representation of local bulk fields in AdS by non-local
operators on the boundary, working in the semiclassical limit and using AdS_2
as our main example. In global coordinates we show that the boundary operator
has support only at points which are spacelike separated from the bulk point.
We construct boundary operators that represent local bulk operators inserted
behind the horizon of the Poincare patch and inside the Rindler horizon of a
two dimensional black hole. We show that these operators respect bulk locality
and comment on the generalization of our construction to higher dimensional AdS
black holes.
