This article discusses key concepts within enactivist writing, focussing especially on concepts involved in the enactivist description of cognition as embodied action: perceptually guided action, embodiment, and structural coupling through recurrent sensorimotor patterns. Other concepts on which these concepts depend are also discussed, including structural determinism, operational closure, autonomy, autopoiesis, consensual domains, and cognition as effective action. Some related concepts that follow from an enactivist view of cognition are considered, in particular bringing forth a world and languaging. The use of enactivism as a methodology in mathematics education is also outlined. References to mathematics education research reported in this issue and elsewhere are used throughout to provide illustrations.