An interface is rough if the mean square fluctuations of its position diverge at large times and system sizes. This may occur when the interface is driven out of equilibrium in the presence of some noise and the way roughness diverges defines suitable critical exponents. We introduce and discuss extensively two important universality classes: the Edwards–Wilkinson and the Kardar–Parisi–Zhang. The latter has been the subject of renewed interest since it was possible to determine analytically the whole spectrum of fluctuations and it was found an experimental system satisfying such predictions with great accuracy. The last part of the chapter is devoted to nonlocal models, specifically the celebrated Diffusion Limited Aggregation.