We present integrated modelling of steady-state and hybrid scenarios for ITER parameters using several predictive transport codes. These employ models for non-inductive current drive sources in conjunction with various theory-based and semi-empirical transport models. In conjunction with the simulation effort, the current drive models are being evaluated in a series of cross-code and code-experiment comparisons under ITER-relevant conditions. New benchmark evaluations of current drive from injection of neutral beams (NBCD), electron cyclotron waves (ECCD) and lower hybrid waves (LHCD) are reported. Simulations using several transport modelling codes self-consistently calculate the heating and current drive sources using ITER design parameters. Operating constraints are also taken into account, although the calculations reported here still require further refinement. The modelling addresses both the final stationary state and dynamic access to it. The simulations indicate that generation and control of internal and edge barriers to access and maintain high confinement will be a major undertaking for future simulations, as well as a challenge for the ITER steady-state and hybrid experimental programme.