The physics basis of a simulation model for lower hybrid current drive (LHCD) is discussed. Issues associated with LH power deposition-wave propagation, mode conversion and cut-offs in toroidal geometry, as well as linear and quasi-linear Landau damping-are analysed. A simulation model (ACCOME) is applied to the LHCD experiment now operating on the Tokamak de Varennes (TdeV). The profiles and values of density and temperature needed as inputs to ACCOME are taken from the experiment. The predictions of current density and loop voltage from ACCOME are then compared with experimental LHCD results. Possible LH current profile control experiments are also analysed for TdeV using composite LH spectra to control the location of RF power deposition. Finally the relevance of these current profile control results to future devices is discussed and an example is shown for ITER-like parameters