Understanding the mechanism that causes the emergence of magnetic flux from the solar interior to the atmosphere, the drastic changes in the properties of the matter and magnetic fields along the rise and the interplay of dynamic and resistive phenomena that shape the emerged regions is one of the major open tasks in solar physics. Important advances are being made both in the theoretical modelling and in the observation of the emergence events. This review concentrates on recent advances through 3D numerical experiments carried out with massively parallel MHD and radiative transfer codes.