The primitive equations are derived from the 3D-Navier-Stokes equations assuming a hydrostatic balance. This is used in meteorological and climate models. In this chapter we give an overview on two instances of stochastic primitive equations. First the primitive equations subject to transport noise and second, the primitive equations with stochastic boundary conditions. Our strategy relies on a combination of deterministic and stochastic maximal \(L^p\) -regularity methods as well as energy methods to prove global well-posedness. Here, we focus on the overall strategy where the explicit proofs can be found in the original articles.