Semantic cognition refers to our ability to use, manipulate and generalize knowledge that is acquired over the lifespan to support innumerable verbal and non-verbal behaviours. This Review summarizes key findings and issues arising from a decade of research into the neurocognitive and neurocomputational underpinnings of this ability, leading to a new framework that we term controlled semantic cognition (CSC). CSC offers solutions to long-standing queries in philosophy and cognitive science, and yields a convergent framework for understanding the neural and computational bases of healthy semantic cognition and its dysfunction in brain disorders.