The processing of materials with unique electronic, mechanical, optical and thermal properties plays a crucial role in modern technology. The quality of these materials depend strongly on the microstructures and the solute/dopant fields in the solid product, that are strongly influenced by the intricate coupling of heat and mass transfer and melt flow in the growth systems. An integrated research program is developed that include precisely characterized experiments and detailed physical and numerical modeling of the complex transport and dynamical processes. Direct numerical simulation of the solidification process is carried out that takes into account the unsteady thermo-solutal convection in the vertical Bridgman crystal growth system, and accurately models the thermal interaction between the furnace and the ampoule by appropriately using experimentally measured thermal profiles. The flow instabilities and transitions and the nonlinear evolution following the transitions are investigated by time series and flow pattern analysis. A range of complex dynamical behavior is predicted with increasing thermal Rayleigh number. The route to chaos appears as: steady convection → transient mono-periodic → transient bi-periodic → transient quasiperiodic → transient intermittent oscillation-relaxation → stable intermittent oscillation-relaxation attractor;The spatio-temporal dynamics of the melt flow is found to be directly related to the spatial patterns observed experimentally in the solidified crystals. The application of the model to two phase Sn-Cd peritectic alloys showed that a new class of tree-like oscillating microstructure develops in the solid phase due to unsteady thermo-solutal convection in the liquid melt. These oscillating layered structures can give the illusion of band structures on a plane of polish. The model is applied to single phase solidification in the Al-Cu and Pb-Sn systems to characterize the effect of convection on the macroscopic shape and disorder in the primary arm spacing of the cellular/dendritic freezing front. The apparently puzzling experimental observation of higher disorder in the weakly convective Al-Cu system than that in the highly convective Pb-Sn system is explained by the numerical calculations.