The operation of the most promising concept for the future fusion rector, tokamak, relies on the generation of plasma current. Traditionally, this is created by magnetic induction which makes the tokamak operation pulsed. With electro-magnetic waves, in the range of the electron cyclotron (EC) frequency of the plasma electrons, current can be driven non-inductively. This provides the possibility of a continuous tokamak operation. In the TCV tokamak, a fully non-inductive operation is a routine experiment. This allows not only the possibility to study the non-inductive tokamak operation, but also the EC wave driven current is easily measurable. In addition, the plasma confinement has been observed to improve when the EC waves drive current in certain locations inside the plasma. This mode of operation is called the internal transport barrier (ITB) and it has been attainable in TCV since 2002. It is assumed that a specific shape of the current density profile causes the ITB to form. However, in TCV no measurement of the current density profile is available. Theoretically, the linear modeling of EC wave driven current fails in some cases to reproduce the experimentally observed current. In addition, TCV is expected to operate on the quasilinear regime. Yet the predicted quasilinear enhancement in the efficiency of the EC wave driven current is not observed, the simulated current being too large by a factor up to ten. These facts suggest that in traditional modeling some important mechanism is missing. For these reasons, modeling experiments where the plasma current is driven by EC waves is an interesting challenge. In this thesis we assume that radial transport of electrons is the missing part in the models. Transport acts as a partially linearizing mechanism in bringing the theoretical current to the observed level. Radial transport also causes current diffusion, affecting strongly the current density profile. Various experiments including non-inductive operation, plasmas with a varying fraction of inductive current, and the ITB mode have been modeled with this technique. The simulated results are consistent with respect to many measured plasma parameters: the driven current, the total plasma energy, the temperature profile, and the observed hard X-ray spectra. In addition, the transport level is in agreement with the experimental limit. Also, in ITB plasmas, the resulting current density profile is in agreement with the theories of ITB formation. These results show that radial transport has a major role in EC wave driven current experiments in TCV. Therefore, only quasilinear simulations taking into account radial transport effects provide the correct experimental results in all cases in TCV.