  Fast radio bursts (FRBs) are recently discovered mysterious single pulses of
radio emission, mostly coming from cosmological distances ($\sim 1$ Gpc). Their
short duration, $\sim 1$ ms, and large luminosity evidence coherent emission. I
review the basic physics of coherent emission mechanisms proposed for FRBs. In
particular, I discuss the curvature emission of bunches, the synchrotron maser,
and the emission of radio waves by variable currents in the course of magnetic
reconnection. Special attention is paid to magnetar flares as the most
promising sources of FRBs. Non-linear effects are outlined that could place
bounds on the power of the outgoing radiation.
