To maintain a high-performance, long-duration tokamak plasma scenario, it is necessary to maintain desired profiles while respecting operational limits. This requires real-time estimation of the profiles, monitoring of their evolution with respect to predictions and known limits, and their active control to remain within the desired envelope. Model-based techniques are particularly suitable to tackle such problems due to the nonlinear nature of the processes and the tight coupling among the various physical variables. A suite of physics-based, control-oriented models for the core plasma proles in a tokamak is presented, with models formulated in such a way that powerful methods from the systems and control engineering community can be leveraged to design ancient algorithms. We report on new development and applications of these models for real-time reconstruction, monitoring and integrated control of plasma proles on TCV, ASDEX-Upgrade and simulations for ITER.