In recent years, advances in computing power and computational methods have made it possible to perform detailed simulations of the coronary artery stenting procedure and of related virtual tests of performance (including fatigue resistance, corrosion and haemodynamic disturbance). Simultaneously, there has been a growth in systematic computational optimisation studies, largely exploiting the suitability of surrogate modelling methods to time-consuming simulations. To date, systematic optimisation has focussed on stent shape optimisation and has re-affirmed the complexity of the multi-disciplinary, multi-objective problem at hand. Also, surrogate modelling has predominantly involved the method of Kriging. Interestingly, though, optimisation tools, particularly those associated with Kriging, haven't been used as efficiently as they could have been. This has especially been the case with the way that Kriging predictor functions have been updated during the search for optimal designs. Nonetheless, the potential for future, carefully posed, optimisation strategies has been suitably demonstrated, as described in this review.