Different experimental techniques, such as kinetic studies of ligand binding and fluorescence correlation spectroscopy, have revealed that the diffusive, internal dynamics of proteins exhibits autosimilarity on the time scale from microseconds to hours. Computer simulations have demonstrated that this type of dynamics is already established on the much shorter nanosecond time scale, which is also covered by quasielastic neutron scattering experiments. The autorsimilarity of protein dynamics is reflected in long-time memory effects in the underlying diffusion processes, which lead to a non-exponential decay of the observed time correlation functions. Fractional Brownian dynamics is an empirical model which is able to capture the essential aspects of internal protein dynamics. Here we give a brief introduction into the theory and show how the model can be used to interpret neutron scattering experiments and molecular dynamics simulation of proteins in solution under hydrostatic pressure.