Decision-making behaviour is studied in many very different fields, from medicine and economics to psychology and neuroscience, with major contributions from mathematics and statistics, computer science, AI and other technical disciplines. However the conceptualisation of what decision-making is and methods for studying it vary greatly and this has resulted in fragmentation of the field. A theory that can accommodate various perspectives may facilitate interdisciplinary working. We present such a theory in which decision-making is articulated as a set of canonical functions that are sufficiently general to accommodate diverse viewpoints, yet sufficiently precise that they can be instantiated in different ways for specific theoretical or practical purposes. The canons cover the whole decision cycle, from the framing of a decision based on the goals, beliefs, and background knowledge of the decision maker to the formulation of decision options, establishing preferences over them, and making commitments. Commitments can lead to the initiation of new decisions and any step in the cycle can incorporate reasoning about previous decisions and the rationales for them, and lead to revising or abandoning existing commitments. The theory situates decision making with respect to other high-level cognitive capabilities like problem-solving, planning and collaborative decision-making. The canonical approach is assessed in three domains: cognitive and neuro-psychology, artificial intelligence, and decision engineering.