Neural oscillations are ubiquitously observed in the mammalian brain, but it has proven difficult to tie oscillatory patterns to specific cognitive operations. Notably, the coupling between neural oscillations at different timescales has recently received much attention, both from experimentalists and theoreticians. We review the mechanisms underlying various forms of this cross-frequency coupling. We show that different types of neural oscillators and cross-frequency interactions yield distinct signatures in neural dynamics. Finally, we associate these mechanisms with several putative functions of cross-frequency coupling, including neural representations of multiple environmental items, communication over distant areas, internal clocking of neural processes, and modulation of neural processing based on temporal predictions.