Heterogeneous Integration provides a powerful and cost-effective means for building complex Systems-in-Package (SiPs). Recently, sophisticated examples of heterogeneously integrated packages containing nearly 50 dies, many fabricated by different vendors on different technological nodes, have been demonstrated. In general, interconnect pitch scaling and integration of large number of dies on a package leads to an exponential increase in material interfaces. Furthermore, the shrinking of the size of vertical interconnects in proportion to the pitch makes them heterogeneous in material phase composition or susceptible to oxide growth at the bond interfaces. Thus, reaction-diffusion problems play a critical role in the reliability of Heterogeneously Integrated packages. In general, numerical modeling can serve as a critical aid to understanding the formation of the phases and their evolution with current or temperature. Two significant challenges to modeling reaction-diffusion problems are the derivation of governing balance laws at the moving interface and developing an efficient computational technique for tracking the motion of the interface. Diffuse interface methods that use implicit geometric description of the interface such as the phase field method is widely used for solving problems with moving interfaces. The disadvantages of implicit interface methods are the complexity of the governing equations in diffuse form, the need for adaptive mesh refinement near the interface and the computational expense due to the implicitization of the geometry. In this study, we describe the derivation of general thermodynamic conditions governing the motion of the interface and develop diffuse as well as sharp interface computational methods to simulate reaction-diffusion problems in general. We then model the growth of Cu-Sn intermetallic compound in microbumps as well as voiding in the solder joint under elevated temperature and current. The models are compared against observations of phase evolution in fabricated test devices.