Abstract: The first objective of this talk will be to present the construction of non-interacting quantum fields on asymptotically anti-de Sitter spacetimes. The crucial ingredient is the holographic Hadamard condition, which ensures Hadamard behaviour in the space-time interior and existence of conformal fields induced at the boundary. In this setting I will explain how holography can be proved on the level of algebras of observables as a consequence of unique continuation theorems (based on joint works with Oran Gannot and Wojciech Dybalski).