Heart disease continues to be a significant clinical problem in Western society. Predictive models and simulations that integrate physiological understanding with patient information derived from clinical data have huge potential to contribute to improving our understanding of both the progression and treatment of heart disease. In particular they provide the potential to improve patient selection and optimisation of cardiovascular interventions across a range of pathologies. Currently a significant proportion of this potential is still to be realised. In this paper we discuss the opportunities and challenges associated with this realisation. Reviewing the successful elements of model translation for biophysically based models and the emerging supporting technologies, we propose three distinct modes of clinical translation. Finally we outline the challenges ahead that will be fundamental to overcome if the ultimate goal of fully personalised clinical cardiac care is to be achieved. A schematic diagram of the relationship between the success factors driving clinical translation of models and the related enabling technologies and tools. These inputs are currently driving model exemplars through three channels. CRT, cardiac resynchronisation therapy; FFR, fractional flow reserve. LVAD, left ventricular assist device.