<p>Computational simulation methods are increasingly used to model the processes that control the formation of hydrothermal ore deposits (HODs) within the Earth’s upper crust. To obtain reliable simulation results, a valid geological model of a HOD is required, then three key challenges must be addressed. The first issue relates to the correct definition of the computational model boundary conditions based on the geological model. The second issue relates to the establishment of a mathematical model to sufficiently describe the chemical and physical processes relevant to HOD formation. The third issue relates to the incorporation of multiple time and spatial scales into the modeling framework. These three issues are often overlooked in many existing studies, potentially leading to inaccurate simulations. This article addresses these issues to ensure that computational modeling of HODs is applied correctly and advances in a scientifically sound direction. In the process of addressing these three issues, it has been demonstrated that: (1) it is possible to use dual spatial-scale procedures, which include both a local deposit model and a regional model, for the determination of the deposit model boundary conditions; (2) in the context of simulating magma solidification processes, a more reliable mathematical model that considers magma phase changes (from liquidus magma to solid rock) should be used to replace commonly used oversimplified models; and (3) the finite element (FE) method and related algorithms are capable of incorporating the multiple temporal and spatial scales required for the simulation of HOD systems.</p>