Abstract: Anti-de Sitter is not a globally hyperbolic spacetime. When studying a field theory on anti-de Sitter, one needs an appropriate choice of boundary conditions at the conformal boundary such that the classical field equation is well-posed. Moreover, at the level of the standard formulation of quantum field theory, the existence of physical quantum states, the so-called Hadamard states, is only guaranteed (and defined) on globally hyperbolic spacetimes. In this talk, I consider a massive scalar field on anti-de Sitter and analyse all of the acceptable boundary conditions, including the commonly used Dirichlet boundary conditions as a particular example. I show that both the classical and quantum field theory is well-defined for these choices and, in particular, we can have a natural definition of a physically relevant, Hadamard state for all choices of boundary conditions.