Nucleation and growth in unary and binary systems is investigated in the framework of the phase-field theory. Evaluating the model parameters from the interfacial free energy and interface thickness, a quantitative agreement is found with computer simulations and experiments on the ice-water system. The critical undercoolings predicted for a simple binary system are close to experiment. Phase-field simulations for isotropic and anisotropic systems show that due to the interacting diffusion fields the Avrami-Kolmogorov exponent varies with transformed fraction and initial concentration. (C) 2002 Elsevier Science B.V. All rights reserved.