After the first surprisingly large 1H DNP enhancements of the water signal in aqueous solutions of nitroxide radicals observed at high magnetic fields, Overhauser DNP is gaining increasing attention for a number of applications now flourishing, showing the potentialities of this mechanism in solution and solid state NMR as well as in MRI. Unexpected Overhauser DNP enhancements in insulating solids were recently measured at 100K, with a magnitude which increases with the applied magnetic field. We recapitulate here the theoretical premises of Overhauser DNP in solution and analyze the effects of the various parameters on the efficacy of the mechanism, underlining the link between the DNP enhancements and the field dependent relaxation properties. Promisingly, more effective DNP enhancements are expected by exploiting the potentialities offered by 13C detection and the use of supercritical fluids.