  The classical Stefan problem is one of the most studied free boundary
problems of evolution type. Recently, there has been interest in treating the
corresponding free boundary problem with nonlocal diffusion.
  We start the paper by reviewing the main properties of the classical problem
that are of interest for us. Then we introduce the fractional Stefan problem
and develop the basic theory. After that we center our attention on selfsimilar
solutions, their properties and consequences. We first discuss the results of
the one-phase fractional Stefan problem which have recently been studied by the
authors. Finally, we address the theory of the two-phase fractional Stefan
problem which contains the main original contributions of this paper. Rigorous
numerical studies support our results and claims.
