In this talk, I will explain how for a contact manifold the existence of a dynamically convex supporting contact form ensures compactness of Floer moduli spaces and thus allows us to define Rabinowitz Floer homology in a symplectisation. In this setting, the Rabinowitz Floer homology groups give a means to deduce existence results of translated points as introduced by Sandon. This is joint work with Matthias Meiwes.