In tokamak plasmas, non-linear interplay between transport and sources/sinks takes place for all transported quantities (current, heat, particles and momentum). Thanks to integrated modelling frameworks, we can iterate physics-based quasilinear turbulent transport models over multiple confinement times. Such modelling allows us to predict current, temperature, density and rotation profiles, and to disentangle the causality at play behind the modelled time evolution. An intense validation effort of such modelling against experimental measurements has been ongoing and has progressed our understanding. In dynamical phases, the so-called 'cold pulse' physics have been explained in the AUG tokamak, the isotope impact in plasma current ramp-up is understood in the JET tokamak, and the impact of the particle source (from neutral beam injection) on tungsten core accumulation has been clarified in JET and AUG. In stationary phases, the saturation of the ion temperature in electron-heated WEST plasmas has been clarified, and the energy content has been predicted with higher accuracy than empirical scaling laws with respect to the plasma current, magnetic field, plasma size and gas fueling, both in L and H modes on AUG. The validation of physics-based integrated modelling allows control optimisation in preparation for ITER operation as well as risk reduction for the design of future reactors. However, despite the reported progress, physics gaps remain on this path. For example, unlike today's devices, ITER-class devices will be opaque to neutrals and fuelled by pellets. In the absence of a physical understanding of the transport in the pedestal, extrapolation is uncertain. Moreover, in burning plasmas, the non-linear coupling between the central core profiles and the fusion power is very strong. The uncertainties in profile predictions due to unverified and unvalidated reduced transport models in such high-pressure plasmas lead to uncertain fusion power predictions. Solutions on how to address these challenges within integrated modelling will be proposed.