Medicine is increasingly complex, involving a highly connected system of people, resources, processes, and institutions. Attempts to improve care involve disruptions to this system, with the potential for wide-ranging consequences, both positive and negative. Despite this, many improvement methodologies are poorly equipped to manage either complexity or risk - instead focusing on discrete interventions whose effects are narrowly monitored. Engineers have long understood that complex problems require a systems view, and that attempts to make things better can themselves introduce new risk into a system. Given this, an engineering systems approach may be of significant value to those trying to improve healthcare. Two fundamental questions emerge from such an approach: what can we do better, and what could possibly go wrong? This paper describes the evolution of a systems approach to healthcare, and explores a recently co-developed framework outlining a systems approach based upon a synergy between healthcare and engineering.