I will present the problem of building local AdS bulk observables from boundary CFT data. Focusing on QFTs coupled to a rigid AdS background, we study the analyticity constraints that bulk locality imposes on bulk-boundary-boundary 3-point functions ("AdS form factors"). We reformulate these constraints as a complete, non-perturbative set of sum rules. These sum rules lead to additional constraints on the boundary CFT on top of crossing, and can be implemented numerically in the bootstrap. We study the flat limit when these "AdS form factors" become form factors. (Based on 2305.07078)