Introduction

Is the core difficulty in the so-called convective term of the equation, i.e. in the simple fact that moving matter is self-advected? In which case, the understanding of threedimensional (3D) incompressible turbulence would be the key to our own case of compressible MHD turbulence (CMT). Or will the many added features – such as Alfvén and magnetosonic waves and a preferred direction in the presence of a strong uniform magnetic field – change the behavior of CMT flows altogether? How far does the concept of universality carry out? This is one of the questions that the detailed observations of astrophysical flows can help settle. In this short review, I shall begin by giving the humongus list of parameters that have to be considered a priori, the rule of the game being to determine which parameters are relevant and which can be ignored. In the next Section, some of the key features of the temporal and spatial development of compressible flows and MHD flows will be recalled. Section 4 is devoted to the formation of large scales (as opposed to small scales), the agent being here the magnetic helicity and Section 5 deals with intermittency and its measure through high-order structure functions.