The kinetic theory of radiofrequency current drive in tokamak plasmas is investigated. The problem of the impact of anomalous transport on the driven current profile and efficiency is considered in detail. Among the possible candidates for explaining anomalous transport in tokamaks, magnetic turbulence is known to have a strong influence on the dynamics of superthermal electrons and is assumed to be the basic mechanism responsible for radial diffusion of the RF-driven current. The 3-dimensional kinetic equation in the presence of RF heating and magnetic turbulence is studied. Its properties are first investigated by a nonlocal response function technique. Both the adjoint formalism and the Langevin equations method are extended to the case of radially diffusing electrons. The full kinetic equation is numerically solved by means of a 3-D Fokker-Planck code. Applications to lower-hybrid current drive are presented and several kinetic effects are discussed.