The phase-field method has become in recent years the method of choice for simulating microstructure formation during solidification. Its chief advantage is to avoid explicit tracking of the solid-liquid interfaces with the help of one or several phase fields, which take constant values in each bulk phase and vary smoothly through diffuse but well-localized interfaces. With recent advances in the formulation of the model and in numerical algorithms, it is now possible to simulate the evolution of complex patterns in three dimensions. However, the results of the simulations generally depend on the width of the diffuse interfaces. Only in a few special cases, namely the symmetric and the one-sided model of solidification, a careful design of the model has made it possible to obtain results that are independent of the interface width for reasonable computational parameters, such that simulations can be quantitatively compared to experiments and theory. This talk will review the ingredients and methods needed to achieve such quantitative phase-field modelling and discuss some possibilities to extend this approach to more general situations.