Analytical and numerical modeling has been developed to predict the solidification microstructure quantitatively in general and grain size in particular. It is found that the interface retardation caused by the solute build-up during solidification significantly influences solute redistribution to create the constitutional undercooling in the liquid which enhance greatly nucleation in the bulk melt. Besides, the solute of silicon has a marked effect on the nucleation chemical driving force in Al-Si alloys, whereas Cu has almost no effect in Al-Cu alloys. A new model for equiaxed solidification, coupled with a macroscopic model for thermal diffusion and microscopic model for the solutions of solute diffusion equations both in the solid and liquid, has been developed. The model is able to predict time-dependent thermal field, solute profiles in both the solid and liquid, solute build-up at the interface and the space-dependent constitutional undercooling in the liquid. The relationship between growth rate and the position of the advancing interface and the cooling conditions are also investigated. A modified Cellular-Automaton (CA) model has been developed and coupled with a control Finite Volume Method (FVM) for calculation of non-uniform temperature domain. The effect of solute redistribution is taken into account for the modeling in two ways: (1) the value of the constitutional undercooling caused by the solute build-up is calculated by the analytical models and then coupled into the continuous nucleation model - this method has the advantages of small amounts of calculations and high computational efficiency but less precision; (2) the solute field is solved numerically - higher precision also with larger calculations. The nucleation parameters for the continuous nucleation model have been investigated systematically and determined carefully. The modeling is then applied for calculation of grain refinement, effect of alloy concentration, simulation of dendritic morphology and prediction of dendrite solidification, nucleation mechanisms, and columnar to equiaxed transition. It significantly enhances the understanding of solidification processing such as the behaviour of solute Ti and grain refiners in pure aluminium and alumimium-silicon alloys, the mechanisms of grain refinement, the possible mechanisms of grain size transition with silicon concentration, competitive growth and selection of dendritic crystals. The mechanisms of grain refinement in pure aluminium and A17SiMg foundry alloy have been proposed based on the investigation of microstructure formation with additives of grain refiners. A concept of "equivalent solute" has been presented to explain why the grain refinement is less effective in foundry alloys. The mechanism of the grain size transition in Al-Si alloys has also been studied.