A full phase field model of eutectic growth is proposed, which incorporates the generic features of a eutectic phase diagram and reduces to the sharp-interface model in the appropriate limit. Large scale two-dimensional simulations are presented for the isothermal solidification of a uniformly undercooled eutectic melt, in which the Avrami exponent is 3. The results of this study identify three possible growth mechanisms: diffusion limited growth, lamellar growth, and spinodal decomposition.