Heat transfer and fluid mechanics of helium flowing in channels are reviewed, Emphasis is placed on observed or anticipated limits of operation which might be expected to apply in applications of superconductivity. Topics included are: the high-heat-flux degradation of heat transfer and possible effects of buoyancy forces in supercritical helium; transition to film boiling in subcritical helium; limiting heat currents in helium II; and the possibility of oscillations in forced flow helium systems.