[en] The high-beta spherical tokamaks (ST), such as NSTX and MAST, are attractive fusion devices for studying the physics of current drive by electron cyclotron (EC) waves. While ST plasmas are overdense to conventional EC waves, electron Bernstein waves (EBW) can be used to generate plasma currents. Besides providing better confinement, EBW driven current can also help suppress neoclassical tearing modes. This paper examines the characteristic features of EBW current drive. It is shown that the propagation and damping of EBWs and their interaction with electrons in STs provides useful insight into the propagation and damping of O waves and their interaction with electrons in ITER. The physics of current drive has also many similar features. A new relativistic wave-particle diffusion operator in toroidal plasmas that includes spatial and momentum transport due to RF waves is derived. It is suitable for numerical implementation and could explain the observed broadening of the current profile due to ECRF waves. The diffusion operator is relevant for studies on heating and current drive by EC waves in present day fusion devices and in ITER. (author)