Abstract: The magnetohydrodynamic technology becomes a research hotspot since the "AJAX" concept was proposed by Russia in the early 1990s. This paper reviews the advances of the studies of magenetohydrodynamic turbulence, mainly in two parts: the characteristics of magenetohydrodynamic turbulence and the numerical models of magenetohydrodynamic turbulence. Magnetohydrodynamic turbulence has some peculiar characteristics such as the anisotropy induced by the magnetic field, the Joule dissipation, the relaminarization of turbulence, which are different from common turbulence. This paper also discusses the effects of the magnetic field on the turbulence structures and the turbulence intensities. Two methods of numerical simulations are addressed for engineering applications: the Reynolds average Navier-Stokes equations and the large eddy simulation. Almost all studies are conducted for incompressible fluid, and it is not the case for aerospace applications since most of air vehicles operate in a medium of high Mach number, that is compressible.