The purpose of this review is to present the state-of-the-art in diagnosis, interpretation and modelling of waves, particles and the magnetic configuration in fusion plasmas. Knowledge of the magnetic configuration underpins all confinement, stability and transport physics, as well as being an essential prerequisite for the inference of plasma parameters from many diagnostics. As the effect of fast particles become important enough to modify the macroscopic variables of the plasma, the macroscopic fluid equations for equilibrium need to be modified to encapsulate the effects of pressure anisotropy, particle and heat flow. We present a review of such modifications in tokamak geometry, and review probabilistic validation techniques of different equilibrium models. In the last decade new spectral tools have also emerged to characterize the linear behaviour of waves and wave-modes, such as SVD, Fourier-SVD, data-mining and the bispectrum. An emerging trend is the use of statistics to characterize the nonlinear wave population of the plasma from wave field data. Finally, progress is reported on developments in understanding the physics of wave–particle resonant interactions, and the emerging science of the wave–particle–plasma interaction.