In spherical tokamaks (ST), the magnetic field strength varies over a wide range across the plasma, and at high betas it deviates significantly from the 1/R dependence of conventional tokamaks. This, together with the high density expected in ST, poses challenging problems for RF heating and current drive. In this paper, the authors investigate the various possible applications of fast waves (FW) in ST. The adjoint technique of calculating current drive is implemented in the raytracing code CURRAY. The applicability of high harmonic and subharmonic FW to steady state ST is considered. They find that high harmonic FW tends to be totally absorbed before reaching the core and may be considered a candidate for off axis current drive while the subharmonic FW tends to be absorbed mainly in the core region and may be considered for central current drive. A difficult problem is the maintenance of current at the startup stage. In the bootstrap ramp-up scenario, the current ramp-up is mainly provided by the bootstrap current. Under this condition, the role of rf becomes mainly the sustainment of plasma through electron heating. Using a slab full-wave code SEMAL, the authors find that the ion-ion-hybrid mode conversion scheme is a promising candidate. The effect of possible existence of edge Alfven resonance and high harmonic cyclotron resonance is investigated and regimes of minimization of edge heating identified.