Wire arc additive manufacturing (WAAM) is a metal additive manufacturing (AM) process attracting interest from the automotive, defence, aerospace, architecture/engineering/construction and other industries because of its ability to manufacture large metal parts cost-effectively. Nevertheless, problems such as part defects and process efficiency remain, and consequently, efforts to improve WAAM are continuing. The WAAM process involves physical phenomena that include fluid flow, heat transfer, phase changes including melting, solidification and vaporization, multi-phase interactions, and deformations resulting from residual stresses-so obtaining a complete understanding is challenging. While numerical modelling is widely used to understand and assist with developing processes, modelling of AM processes such as WAAM is sophisticated because of their multi-physics and multiscale nature. This review addresses the existing and likely future roles of numerical modelling in advancing WAAM technology. Consideration is given to the known problems with WAAM, the different types of numerical modelling, including computational fluid dynamics, the finite element method, and smoothed particle hydrodynamics, and their potential to address persistent issues. Additionally, this review seeks to provide an understanding of the physics associated with the WAAM process, examines the trends in the development of WAAM technology, and recommends possible future directions. These include the combination of different physics-based modelling approaches to overcome their individual shortcomings, and the inclusion of modelling as part of a digital twin of the WAAM process.