Manufacturing of light-weight materials is associated with several types of casting defects during solidification. Porosity defects are common, especially in aluminum and its alloys, which initiate crack propagation and thereby cause drastic deterioration in the mechanical properties. These defects, classified as micro and macro defects (based on their sizes), are mainly governed by release of hydrogen into the liquid at the solid-liquid interface, which triggers the nucleation and growth of hydrogen bubbles in the melt. Subsequently, these bubbles interact with solidifying interfaces such as dendritic arms and eutectic fronts, leading to the formation of pores. Macroscopic defects in the form of voids are created due to solidification shrinkage. The primary focus of the present work is to develop phenomenological models for the evolution of microporosity and microstructures during solidification. The issues outlined above typically occur in multi-phase environments comprising of solid, liquid and gaseous phases, and over a range of length and time scales. Any phenomenological prediction would, therefore, require a multi-phase-scale approach. Principles of volume averaging are applied to equations of conservation to obtain single-field formulations. These are then solved with appropriate interface tracking techniques such as Enthalpy, Level-set, Volume-of-fluid and Immersed-boundary methods. The framework is built up on a standard pressure based incompressible fluid flow solver (SIMPLER algorithm) and coupled modeling strategies are proposed to address the interfacial dynamics. A two-dimensional framework is considered with a fixed-grid Cartesian co-ordinate system. Scaling analyses are performed to bring out the relative effects of various competing parameters in order to obtain further insights into this complex phenomenon. The numerical results and scaling predictions are validated against experimental observations published in literature. In literature, numerical predictions of microporosity mainly include criteria based models based on empirical relations and deterministic/stochastic models based on diffusion driven growth assuming spherical bubbles. The dynamic evolution of non-spherical bubble-metal interface in a three-phase system is yet to be captured. Moreover, several in-situ experiments have shown elongated bubble shapes during the engulfment phase, therefore a criterion to define the dependence on cooling rates and the resulting bubble morphology can possibly deliver further practical insights. We propose a numerical model for hydrogen bubble growth, its movement and subsequent engulfment by a solidifying front, combining the features of level-set and enthalpy methods for tracking bubble-metal and solid-liquid interfaces, respectively. The influx of hydrogen into heterogeneously nucleated bubbles results in growth of bubbles to sizes up to a few hundreds of microns. In the first part of this numerical study, a methodology based on the level-set approach is developed to simultaneously capture hydrogen bubble growth and movement in liquid aluminum. The solidification is first assumed to occur outside the micro-domain providing a specified hydrogen influx to the bubble-in-liquid system. The level-set equation is formulated in such a way as to account for simultaneous growth and movement of the bubble. The growth of a bubble with continuous and fixed hydrogen levels in the melt is studied. The rates of growth of bubble-liquid and solidifying interfaces are compared using an order of magnitude analysis. This scaling analysis explains the thought experiment proposed in the literature, where difference in bubble shapes was attributed to the cooling rate. Moreover, it shows explicit dependence on bubble radius and cooling rate leading to a new criterion for bubble elongation proposed in this thesis. This also highlights the comparison between solidification and hydrogen diffusion time-scales which primarily govern the competitive growth behavior. The bubble-in-liquid model is coupled with microscopic enthalpy method to incorporate effects of solidification and study the interaction of solid-liquid and bubble-liquid interfaces. The phenomena of bubble engulfment and elongation are successfully captured by the proposed model. A parametric study is carried out to estimate the bubble elongation based on different initial bubble sizes and varying cooling rates encountered in typical sand, permanent mold and die casting processes. Although simulation of microstructures has been extensively studied in the literature, very few models address the phenomena of simultaneous growth and movement of equiaxed dendrites. The presence of different flow environments and multiple dendrites are known to alter the position and shape of the dendrites. The proposed model combines the features of the following methods, namely, the Enthalpy method for modeling growth; the Immersed Boundary Method (IBM) for handling the rigid solid-liquid interfaces; and the Volume of Fluid (VOF) method for tracking the advection of the dendrite. The algorithm also performs explicit-implicit coupling between the techniques used. Validation with available literature is performed and dendrite growth in presence of rotational and buoyancy driven flow fields is studied. The expected transformation into globular microstructure in presence of stirring induced flows is successfully simulated. A simple order estimate for time required for stirring is performed which agrees with numerical predictions. In buoyancy driven environment of a settling dendrite, the arm tip speeds show expected higher velocity of the upstream tip compared to its counterpart. The model is extended to study thermal and hydrodynamic interactions between multiple dendrites with appropriate considerations for different orientations and velocities of the dendritic solid entities. The present model can be used for the prediction of grain sizes and shapes and to simulate morphological transformations due to different melt flow scenarios. In the final part, the methodology presented for growth and engulfment of hydrogen bubbles is extended to study the phenomenon of diffusion driven bubble growth occurring in direct foaming of metals. The source of hydrogen is determined by the rate of decomposition of the blowing agent. This is accounted for by a source term in the hydrogen species conservation equation, and growth rate of hydrogen bubbles is calculated on the basis of diffusive flux at the interface. The level-set method is used for tracking the bubble-liquid interface growth, and the macroscopic enthalpy model is used for obtaining heat transfer and solid front position. The model is validated with analytical solution by comparing the front position and the solidification time. The variation of foam density with a transient hydrogen generation source is studied and qualitatively compared with results reported in literature. The modeling strategies proposed in this work are generic and therefore have potential in simulating a variety of complex multi-phase problems.