Understanding the fundamental mechanisms of solidification and the relative significance of different parameters governing these mechanisms is of vital importance for controlling the evolution of microstructure during solidification, and consequently, for improving the efficacy of a casting process. Towards achieving this goal, the present work attempts to study the effect of convection and shrinkage on solidification and microstructure formation primarily through the development of computational models which are complemented with experimental investigations and analytical solutions. Convection strongly influences the solutal and thermal distribution adjacent to the solidification interface and affects the growth rate and morphology of dendrites. To investigate this, a numerical model based on the enthalpy method is developed for binary alloy dendrite growth in presence of convection. The model results are validated with corresponding predictions using level-set method and micro-solvability theory. Subsequently, the model is applied for studying the effect of convection on the growth morphology of single dendrites. Results show that the presence of flow significantly affects the thermo-solutal distribution and consequently the growth rate and morphology of dendrites. Parametric studies performed using the model predict that thermal and solutal Peclet number and melt undercooling strongly influence the tip velocity of dendrites. Additionally, an analytical model is developed to quantify the effect of convection on dendrite tip velocity through the definition of an equivalent undercooling. An expression for this equivalent undercooling is derived in terms of the flow Nusselt and Sherwood numbers and the analytical equivalent undercooling values are compared with corresponding predictions obtained using the numerical model. Subsequently, the interaction of multiple dendrites growing in close proximity is studied. It is observed that the presence of neighbouring dendrites strongly influences the thermo-solutal distribution in the domain leading to significant changes in growth pattern. The effect of seed density on the growth morphology is investigated and it is observed that a higher initial seeding density leads to more spherical dendritic structure. Comparison with results from chilled casting of Al-6.5% Cu alloy with and without grain refiners show qualitative similarity in both the cases. The next part of the thesis presents a eutectic solidification model developed using the general enthalpy-based framework for dendritic solidification. New parameters and rules are defined and suitable modifications are made to incorporate the physics of eutectic solidification and account for the additional complexities arising due to the presence of multiple solid phases. The model simulates the presence of buoyancy driven convection and its interaction with the solidification process. i The model predictions are found to be in good agreement with the Jackson-Hunt theory. At first, the model is applied to simulate regular eutectic growth in a purely diffusive environment and it is observed that the model predicts the variation in interface profile with change in lamella width similar to those observed in experimental studies on eutectic solidification. Subsequently, a few case studies are performed to demonstrate the ability of the model in handling complex scenarios of eutectic growth such as width selection, lamella division and presence of solutal buoyancy. It is observed that solutal buoyancy gives rise to flow cells ahead of the eutectic interface facilitating the transfer of solute between the two phases. Apart from forced and natural convection, another important factor affecting solidification is the presence of shrinkage. Currently, solidification shrinkage is mostly modelled using empirical relations and criteria functions. In the present work, a phenomenological model for shrinkage driven convection is developed by incorporating the mechanism of solidification shrinkage in an existing framework of enthalpy based macro-scale solidification model. The effect of shrinkage flow on the free surface deformation is accounted for by using the volume-of-fluid method. The results predicted by the model are found to be in excellent agreement with analytical solutions for one-dimensional solidification with unequal phase densities. A set of controlled experiments are designed and executed for validating the numerical model. The experiments involve in-situ X-ray imaging of casting of pure aluminium in a rectangular cavity. The numerical predictions for solidification rate, free surface movement and temperature profiles are compared with corresponding experimental results obtained from the in-situ X-ray images and thermocouple data. Subsequent case studies, performed using the model, show significant influence of applied heat flux and mould geometry on the formation of shrinkage cavities. The shrinkage flow model provides the foundation for development of a generalized model to accurately predict the formation and morphology of internal porosity. The validated macro-scale shrinkage model is extended to the microscopic scale to study the influence of shrinkage flow on the growth rate of dendrites. Results demonstrate that shrinkage driven convection towards the dendrite strongly influences the solutal and thermal distribution adjacent to the solidification interface and consequently decreases the growth rate of the dendrite. Additionally, an analytical model is developed to quantify the effect of shrinkage driven convection through the definition of an equivalent undercooling for shrinkage flow. The present models provide significant physical insight into various mechanisms governing the process of solidification. Moreover, due to their similar framework, the individual models have the potential to be an effective foundation for the development of a generalized multi-scale solidification model incorporating the presence of important phenomena such as shrinkage and convection.