In this talk, I will explain how tools from harmonic and functional analysis play a role in the study of stochastic partial differential equations (SPDEs) of parabolic type. In particular, we consider the $H^\infty$-functional calculus, which provides an efficient way to establish well-posedness of linear SPDEs on bounded domains. We do this in the setting of Sobolev spaces with power weights, which measure the distance to the boundary of the domain. These weights suppress singularities of the solution near the boundary. The $H^\infty$-functional calculus on weighted spaces plays an important role in the study of more complicated nonlinear SPDEs on bounded domains. This is joint work with Nick Lindemulder, Emiel Lorist and Mark Veraar.