This proceedings paper reports on the theoretical modelling of particle acceleration in magnetised turbulent plasmas. It briefly reviews some recent findings obtained from fully kinetic numerical simulations of large-amplitude, semi to fully relativistic turbulence. The paper then argues that these findings can be understood within the framework of a ``generalised Fermi'' picture of stochastic acceleration, which it summarises. The dominant contributions to acceleration appear to arise from particle interactions with sharp, dynamic bends of the magnetic field lines and regions of velocity compression. Interestingly, the acceleration rate is spatially inhomogeneous and its probability distribution follows a broken power law extending up to large values. This makes relativistic, large-amplitude turbulence an extreme particle accelerator. Some implications for particle transport and the shape of the particle energy spectrum in the presence of radiative losses and over long timescales are also discussed.