Cross-frequency coupling (CFC), in other words the association of multiple frequency neural oscillations, is present across different frequency bands and neural systems. Circuit mechanisms determine CFC characteristics: oscillations generated in distinct versus overlapping circuits, and continuously active versus intermittent fast oscillation (FO). Dynamic network properties determine CFC signatures: phase–phase coupling occur under weakly coupling and do not co-occur with phase–frequency coupling; phase–amplitude coupling is present when the FO is intermittent or sparse spiking; amplitude–amplitude coupling requires asymmetrical slow oscillations. CFC is mechanistically implicated in three cognitive operations: multi-item representation, long-distance communication, and stimulus parsing. Modeling shows that theta–gamma CFC is an intracortical mechanism for parsing speech.