A general decomposition of the spectral tensor of double velocity correlations in terms of `energy, polarization, helicity' has been proposed for homogeneous, arbitrarily anisotropic, fluid turbulence. Dynamical `exact' equations, generalizing the Lin equation in HIT, display typical nonlinear contributions (spectral transfers) to these terms. This approach is extended to MHD flows, accounting for all the correlations for the magnetic field and their cross-correlations with the velocity field. Linear dynamics is revisited in the presence of a strong external magnetic field, with and without rapid rotation, in order to illustrate the development of the various spectral descriptors. The role of nonlinearity is displayed by comparing full DNS results to the preceding 'linear' ones. The `alpha-effect', introduced by K. Moffatt in the quasi-isotropic case, is finally discussed following the new anisotropic approach. In addition, a new insight is given to relevant anisotropic spectra, namely those of energy (kinetic and magnetic), helicity, cross-helicity and electromotive force.