The broad interest in rapid solidification processes originates from the variety of non-equilibrium microstructures found in the solidified materials; most familiar examples are dendrites, lamellar eutectics, cellular and banded structures. In spite of the deep efforts devoted to this subject by the scientific community, the interfacial dynamics is far from being well understood. The aim of this article is to review some recent theoretical developments, which give a diffuse picture of the interfacial region. A new microscopic approach, based on the stochastic dynamics of a lattice of Potts spins, is also discussed.