Episodic memory must accomplish two adversarial goals: encoding and storing a multitude of experiences without exceeding the finite neuronal structure of the brain, and recalling memories in vivid detail. Dimensionality reduction and expansion ('dimensionality transformation') enable the brain to meet these demands. Reduction compresses sensory input into simplified, storable codes, while expansion reconstructs vivid details. Although these processes are essential to memory, their neural mechanisms for episodic memory remain unclear. Drawing on recent insights from cognitive psychology, systems neuroscience, and neuroanatomy, we propose two accounts of how dimensionality transformation occurs in the brain: structurally (via corticohippocampal pathways) and functionally (through neural oscillations). By examining cross-species evidence, we highlight neural mechanisms that may support episodic memory and identify crucial questions for future research.