Critical illness, a constellation of interrelated inflammatory and physiological derangements occurring subsequent to severe infection or injury, affects a large number of individuals in both developed and developing countries. The prototypical complex system embodied in critical illness has largely defied therapy beyond supportive care. We have focused on the utility of data-driven and mechanistic computational modelling to help address the complexity of critical illness and provide pathways towards discovering potential therapeutic options and combinations. Herein, we review recent progress in this field, with a focus on both animal and computational models of critical illness. We suggest that therapy for critical illness can be posed as a model-based dynamic control problem, and discuss novel theoretical and experimental approaches involving biohybrid devices aimed at reprogramming inflammation dynamically. Together, these advances offer the potential for Model-based Precision Medicine for critical illness.