Our project investigates the possibility of a unified theory of practical understanding and theoretical understanding, as paradigmatically exemplified in skillful activity and scientific achievement, respectively. The project has four components. The first is an examination of basic similarities and differences between practical and theoretical understanding; we pursue the idea that both fundamentally involve an appropriate conception of whatever is understood—an attitude whose possession constitutes a kind of objective, intelligent, robust, epistemic achievement. The second component is an account of the metaphysics and epistemology of conceptions: in particular, their structure, formation, and potential for change and evolution. The third component is a non-propositional semantics for objectual understanding and understanding-wh (why, who, where, when, and how). In addressing these issues, we hope to gain insight into the nature, variety, and growth of understanding, and perhaps also to shed light—as a fourth component—on the notions of intellectual progress and wisdom.