Plasma spray is one of the most versatile and established techniques for the deposition of thick coatings that provide functional surfaces to protect or improve the performance of the substrate material. However, a greater understanding of plasma spray torch operation will result in improved control of process and coating properties and in the development of novel plasma spray processes and applications. The operation of plasma torches is controlled by coupled dynamic, thermal, chemical, electromagnetic, and acoustic phenomena that take place at different time and space scales. Computational modeling makes it possible to gain important insight into torch characteristics that are not practically accessible to experimental observations, such as the dynamics of the arc inside the plasma torch. This article describes the current main issues in carrying out plasma spray torch numerical simulations at a high level of fidelity. These issues encompass the use of non-chemical and non-thermodynamic equilibrium models, incorporation of electrodes with sheath models in the computational domain, and resolution of rapid transient events, including the so-called arc reattachment process. Practical considerations regarding model implementation are also discussed, particularly the need for the model to naturally reproduce the observed torch operation modes in terms of voltage and pressure fluctuations.