Abstract. Non-interacting brownian particles follows Langevin equations fullfiling fluctuation–dissipation relation between friction and thermal noise. Under a linear potential (constant force) Einstein found a relation between diffusion and transport through mobility. In nonlinear potentials this prediction is only satisfied within the limit of very large constant external forces. Moreover, other more interesting behaviors do appear, such as: dispersionless transport, sorting, giant diffusion, subdiffusion, superdiffusion, subtransport, etc. All these phenomena depend on the characteristics of the nonlinear potential landscape: periodic or random, the symmetries and boundary conditions. Moreover, the presence of transport is the keystone of most of this phenomenology. In this review we present numerical simulations of these facts and theoretical analysis when possible