This review article examines the last decade of studies investigating solid, molten, and liquid particle interactions with one another and with walls in heterogeneous multiphase flows. Such flows are experienced in state-of-the-art and future-concept gas turbine engines, where particles from the environment, including volcanic ash, runway debris, dust clouds, and sand, are transported by a fluid carrier phase and undergo high-speed collisions with high-temperature engine components. Sand or volcanic ash ingestion in gas turbine engines is known to lead to power-loss and/or complete engine failure. The particle-wall interactions that occur in high-temperature sections of an engine involve physics and intrinsic conditions that are sufficiently complex that they result in highly disparate and transient outcomes. These particles, which often times are made up of glassy constituents called calcium–magnesium–alumino–silicate (CMAS), are susceptible to phase change at combustor temperatures (1650°), and can deposit on surfaces, undergo elastic and plastic deformation, rebound, and undergo breakup. Considerable research has been put into developing empirical and physics-based models and numerical strategies to address phase interactions. This article provides a detailed account of the conceptual foundation of physics-based models employed to understand the behavior of particle-wall interaction, the evolution of numerical methods utilized for modeling these interactions, and challenges associated with improving models of particle-particle and particle-wall interactions needed to better characterize multiphase flows. It also includes description of a testbed for acquiring canonical data for model validation studies.