Abstract
In this paper we review the current state-of-the-art in the modeling of solidification by phase-field models. We briefly review the phase-field formulation of the solidification of a pure material and discuss how important physical effects, such as surface energy anisotropy, may be included. We go on to discuss numerical solutions of the phase-field equations, with particular reference to the computation of dendrites. Finally, we describe recent successful attempts to extend the phase-field methodology to alloys.
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