Can we understand Alfvenic turbulence via simulations of the MHD equations?

Solar wind turbulence in the range between one day and several minutes may be looked at in different ways: on the one side MHD turbulence in a mean magnetic field, on the other almost freely propagating waves, with wave fronts being distorted by the streams and large-scale transverse magnetic gradients, and stretched by the mean diverging flow. We review some of the relevant numerical work and phenomenology. In particular, we propose a phenomenology of homogeneous MHD turbulence with a mean magnetic field (based on Iroshnikov-Kraichnan's ideas) in which the spectrum exhibits some anisotropy, not in the spectral index, but in the inertial range extent. In the solar wind, the situation is far from this highly idealized one; one of the main problems is that of the competition between the symmetries around two different axes: mean field and radial direction.