This paper reviews the recent advancements in computational modelling of the lubrication of hip and knee joint replacements, especially those concerning Professor Duncan Dowson's contribution. The review starts with the development of modelling the five key parameters that appeared in the pioneered Hamrock-Dowson formula. Then, the theory and approaches for the mixed lubrication in which the artificial hip and knee joint replacements operate are reviewed. We also discuss the current challenges in modelling the lubrication behaviour of joint replacements and how these challenges could be addressed in future studies. These challenges include the mixed lubrication theory, the numerical complexities due to complicated realistic geometry, material and rheology, and individual physiological diversities.