Titanium alloys, which are endowed with excellent properties of low density and high strength, have broad application prospects in the field of aerospace structural components. However, traditional manufacturing methods are constrained by the intrinsic characteristics of titanium alloys, such as high melting points and low thermal conductivity, resulting in exorbitant production costs and thus limiting their large-scale application. As a mainstream metal additive manufacturing technology, selective laser melting (SLM) leverages the process advantage of layer-by-layer deposition to enable precision fabrication of complex structural components, providing an effective solution to the processing challenges of titanium alloys while promising reduced production costs and enhanced production efficiency. Nevertheless, the SLM process involves a nonequilibrium physical metallurgical process encompassing light-to-heat energy conversion and material phase transformation, where microscopic physical phenomena are difficult to observe directly. Moreover, experimental process optimization via the trial-and-error approach suffers from long cycles and high costs, whereas numerical simulation  has become a crucial means to uncover the intrinsic process mechanisms and drive the rational design of processes. Focusing on the forming process of SLM-fabricated titanium alloys, this paper comprehensively reviews the research progress in multiphysics field simulations and methodologies, defect prediction and control, and microstructure evolution simulations. The principles, advantages and applicable scenarios of different simulation methods are analysed. Finally, on the basis of an in-depth analysis of current relevant research, the numerous challenges remaining in the field of simulation studies on selective laser melting of titanium alloys are summarized, and prospects are proposed. Key words： selective laser melting; multiphysics field simulation; defect prediction and control; microstructure evolution; titanium alloys