Experiments on single particle tracking in biological and artificial membranes and in living cells show that the particle's diffusion in such surroundings is often anomalous, showing strong deviations from the Fick's law predicting the mean squared displacement growing as the first power on time. In the present talk we concentrate on systems showing subdiffusive behavior. After discussing pertinent situations we will try to give a classification of anomalous diffusion regimes based on physical reasons in search for the order in the large Zoo of corresponding mathematical models. Our discussion will concentrate on the connection of anomalous diffusion with the type of disorder through which the intrinsic complexity of the system is described when passing from a physical to a mathematical model. We moreover discuss practical methods for disentangling the influences of structural and energetic disorder in pure cases and for anomalous diffusion of the mixed origins.