This contribution gives a short introduction into the theory of anomalous diffusion and relaxation with illustrations from computer simulations of biomolecular systems. The theory is presented from the perspective of the non-equilibrium statistical physics, confronting stochastic models with exact results which have been recently obtained on the basis of asymptotic analysis. In this context, conditions for anomalous diffusion will be discussed and the Kubo relations for the fractional diffusion and relaxation constant will be derived.