Metal powder bed fusion (MPBF) is not a standalone process, and other manufacturing technologies, such as heat treatment and surface finishing operations, are often required to achieve a high-quality component. To optimise each individual process for a given component, its progression through the full process chain must be considered and understood, which can be achieved through the use of validated models. This article aims to provide an overview of the various modelling techniques that can be utilised in the development of a digital twin for MPBF process chains, including methods for data transfer between physical and digital entities and uncertainty evaluation. An assessment of the current maturity of modelling techniques through the use of technology readiness levels is conducted to understand their maturity. Summary remarks highlighting the advantages and disadvantages in physics-based modelling techniques used in MPBF research domains (i.e. prediction of: powder distortion; temperature; material properties; distortion; residual stresses; as well as topology optimisation), post-processing (i.e. modelling of: machining; heat treatment; and surface engineering), and digital twins (i.e. simulation of manufacturing process chains; interoperability; and computational performance) are provided. Future perspectives for the challenges in these MPBF research domains are also discussed and summarised.