In vitro and in vivo testing can provide insight into knee joint mechanics and implant performance. However, these methods are costly and time-consuming, which always limits their widespread use during the design stage of the implant. This review presents a critical analysis of computational modelling (in-silicon) techniques including (i) development of a generic model of total knee replacement (TKR) and application of material properties, loading, and boundary conditions;​ (ii) design and execution of computational experiments;​ and (iii) practical applications and significant findings. The results show that the generic model and techniques provide significant insight into the general performance of TKR but have limited explicit validation. The introduction of design-of-experiments, probabilistic, and neural network methodologies in computational modelling has enabled simulation at the population level. Further advances in subjective modelling appear to be limited, mainly because of the lack of subjective materials and boundary conditions. Computational modelling will increasingly be used in the preclinical testing and design of TKR. This modelling should include subjective, multi-scale, and closely corroborated analyses to account for the variability of TKR.