Shapes of cognition is a new conceptual paradigm for the computational cognitive modeling of Language-Endowed Intelligent Agents (LEIAs). Shapes are remembered constellations of sensory, linguistic, conceptual, episodic, and procedural knowledge that allow agents to cut through the complexity of real life the same way as people do: by expecting things to be typical, recognizing patterns, acting by habit, reasoning by analogy, satisficing, and generally minimizing cognitive load to the degree situations permit. Atypical outcomes are treated using shapes-based recovery methods, such as learning on the fly, asking a human partner for help, or seeking an actionable, even if imperfect, situational understanding. Although shapes is an umbrella term, it is not vague: shapes-based modeling involves particular objectives, hypotheses, modeling strategies, knowledge bases, and actual models of wide-ranging phenomena, all implemented within a particular cognitive architecture. Such specificity is needed both to vet our hypotheses and to achieve our practical aims of building useful agent systems that are explainable, extensible, and worthy of our trust, even in critical domains. However, although the LEIA example of shapes-based modeling is specific, the principles can be applied more broadly, giving new life to knowledge-based and hybrid AI.