A major challenge in toxicology is the development of non-animal methods for the assessment of human health risks that might result from repeated systemic exposure. We present here a perspective that considers the opportunities that computational modelling methods may offer in addressing this challenge. Our approach takes the form of a commentary designed to inform responses to future calls for research in predictive toxicology. It is considered essential that computational model-building activities be at the centre of the initiative, driving an iterative process of development, testing and refinement. It is critical that the models provide mechanistic understanding and quantitative predictions. The aim would be to predict effects in humans; in order to help define a challenging but yet feasible initial goal the focus would be on liver mitochondrial toxicity. This will inevitably present many challenges that naturally lead to a modular approach, in which the overall problem is broken down into smaller, more self-contained sub-problems that will subsequently need to be connected and aligned to develop an overall understanding. The project would investigate multiple modelling approaches in order to encourage links between the various disciplines that hitherto have often operated in isolation. The project should build upon current activities in the wider scientific community, to avoid duplication of effort and to ensure that investment is maximised. Strong leadership will be required to ensure alignment around a set of common goals that would be derived using a problem-statement driven approach. Finally, although the focus here is on toxicology, there is a clear link to the wider challenges in systems medicine and improving human health.JRC.I.5-Systems Toxicolog