Wetting, phase change, and reaction in high temperature systems (e.g., a liquid metal on a metal substrate) are complex phenomena that are only partially understood. These phenomena occur in joining processes, thin film processing and sintering among others. Dissolutive wetting is characterized by chemical and physical processes that span a broad range of spatial and temporal scales. While experiments are difficult to conduct, there have been a number of experimental investigations of dissolutive wetting in metal-metal systems and a short review of these studies is presented. Although limited, recently there have been studies comparing results, such as spreading rate and dissolution depth, from experiments to those from computational simulations. For dissolutive wetting in metal systems it is difficult to observe much of the spreading process experimentally. Computational models may provide better understanding of many aspects of dissolutive wetting. Models of dissolutive wetting incorporate knowledge from chemical thermodynamics, phase transformations, capillary behavior, and multi-phase transport. A number of computational models have appeared in the literature over the last 10 years. Dissolutive wetting has been studied using a broad range of approaches from molecular dynamics to continuum based models at the drop scale that include hydrodynamic transport using different levels of sophistication. We present a comprehensive review of the modeling approaches that have been used to study dissolutive wetting.