In order to prepare adequate current ramp-up and ramp-down scenarios for ITER, present experiments from various tokamaks have been analysed by means of integrated modelling in view of determining relevant heat transport models for these operation phases. A set of empirical heat transport models for L-mode (namely, the Bohm–gyroBohm model and scaling based models with a specific fixed radial shape and energy confinement time factors of H96−L = 0.6 or HIPB98 = 0.4) has been validated on a multi-machine experimental dataset for predicting the li dynamics within ±0.15 accuracy during current ramp-up and ramp-down phases. Simulations using the Coppi–Tang or GLF23 models (applied up to the LCFS) overestimate or underestimate the internal inductance beyond this accuracy (more than ±0.2 discrepancy in some cases). The most accurate heat transport models are then applied to projections to ITER current ramp-up, focusing on the baseline inductive scenario (main heating plateau current of Ip = 15 MA). These projections include a sensitivity study to various assumptions of the simulation. While the heat transport model is at the heart of such simulations (because of the intrinsic dependence of the plasma resistivity on electron temperature, among other parameters), more comprehensive simulations are required to test all operational aspects of the current ramp-up and ramp-down phases of ITER scenarios. Recent examples of such simulations, involving coupled core transport codes, free-boundary equilibrium solvers and a poloidal field (PF) systems controller are also described, focusing on ITER current ramp-down.