Abstract : The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement (MSD) that grows linearly with time, can be broken under diverse realistic conditions. The Gaussian shape is preserved in fractional Brownian motion or scaled diffusion, while diffusion is anomalous, i.e. MSD t^α with α ≠ 1. In Brownian yet non-Gaussian diffusion, the non-Gaussian shape is accompanied by the standard MSD. For instance, non-Gaussianity can emerge due to intrinsic heterogeneity of the tracers or the environment, as a consequence of the superstatistics of diffusivities. The seminar will provide a discussion of the current modellings and interpretations of some generalized diffusions.