Episodic memory retrieval is thought to rely on the replay of past experiences, yet it remains unknown how human single-unit activity is temporally organized during episodic memory encoding and retrieval. We found that ripple oscillations in the human cortex reflect underlying bursts of single-unit spiking activity that are organized into memory-specific sequences. Spiking sequences occurred repeatedly during memory formation and were replayed during successful memory retrieval, and this replay was associated with ripples in the medial temporal lobe. Together, these data demonstrate that human episodic memory is encoded by specific sequences of neural activity and that memory recall involves reinstating this temporal order of activity.