The holographic principle is puzzling: how can it be that degrees of freedom on the boundary of a spacetime region give rise to approximately local physics in the interior? I will review some aspects of the emergence of local AdS physics from the boundary field theory and then discuss a construction of boundary operators that measure local bulk observables. The construction provides a nice way to understand some paradoxical features of the AdS/CFT duality. In addition it may give some hints about holography with different boundaries.