The effort to identify the properties of fusion burning plasmas, involving issues of basic plasma physics and new revealing experimental observations, has led to the development of a theoretical basis for three relevant subjects: (i) novel features of the quasi-coherent mode (QCM) associated with the H-confinement regime, (ii) magnetic reconnection processes in low collisionality regimes and the theory of unpredicted macroscopic modes producing magnetic islands with a propagating velocity in the ion diamagnetic velocity direction, (iii) angular momentum transport described by a non-diffusive equation reproducing the spontaneous rotation velocity profiles; the plasma modes that are identified can produce an angular momentum transport contrary to that predicted by a diffusion process and involve significant electron temperature fluctuations.