In this thesis we analyze the temporal evolution and the physical properties of small-scale flux in sunspot penumbrae. The penumbra is a magnetized medium where convection should be inhibited. However, it is observed as a plethora of bright filaments of different sizes that evolve in a few minutes, leading us to ask how matter moves in the penumbra. Since the discovery of the Evershed ow in 1909, theoretical models and observational studies have attempted to explain what it is happening in the penumbra, but none have totally explained observations. Recently, 3D MHD simulations have enable us to test models and to compare them with observations. Results from the latest published simulations support overturning convecti...