Random dynamical systems are very important in many applications. We are interested in the long--time--behaviour of these systems.In this work, the dynamics of stochastic partial differential equations with dynamical boundary conditions are investigated. At first, we consider random attractors of parabolic equations with additive and multiplicative noise. The main result of this section is the existence of an attractor of the Boussinesq system with dynamical boundary conditions. Then, we show the existence of an inertial manifold of these equations. Finally, the existence of a random attractor of a hyperbolic stochastic partial differential equation with multiplicative noise is proven. In this chapter, a new method, based on mild solutions, is additionally used.