Human cognition is unique in its ability to perform a wide range of tasks and to learn new tasks quickly. Both abilities have long been associated with the acquisition of knowledge that can generalize across tasks and the flexible use of that knowledge to execute goal-directed behavior. We investigate how this emerges in a neural network by describing and testing the Episodic Generalization and Optimization (EGO) framework. The framework consists of an episodic memory module, which rapidly learns relationships between stimuli; a semantic pathway, which more slowly learns how stimuli map to responses; and a recurrent context module, which maintains a representation of task-relevant context information, integrates this over time, and uses it both to recall context-relevant memories (in episodic memory) and to bias processing in favor of context-relevant features and responses (in the semantic pathway). We use the framework to address empirical phenomena across reinforcement learning, event segmentation, and category learning, showing in simulations that the same set of underlying mechanisms accounts for human performance in all three domains. The results demonstrate how the components of the EGO framework can efficiently learn knowledge that can be flexibly generalized across tasks, furthering our understanding of how humans can quickly learn how to perform a wide range of tasks—a capability that is fundamental to human intelligence.