Incompressible magnetohydrodynamics (MHD) provides the simplest theoretical framework for understanding magnetised plasma turbulence, which plays an important role in many problems in astrophysics, space physics and laboratory plasma physics. Numerical simulations of MHD turbulence are of great value, but the Reynolds numbers that are attainable are far below those relevant to nature. There is therefore much interest in building phenomenological models to understand the universal scaling properties of the small-scale fluctuations.

In this talk I shall describe how high-resolution numerical simulations coupled with phenomenological modelling can be very useful for gaining insight into the basic properties of MHD turbulence (e.g. the process of scale-dependent alignment of the velocity and the magnetic field fluctuations (Boldyrev, 2006)). I will also discuss how the Kolmogorov self-similarity hypotheses for the universal structure of the inertial and dissipation intervals of hydrodynamic turbulence do not pass over easily into the MHD case, and how this imposes stringent resolution requirements on numerical studies of MHD turbulence.