We review recent results obtained in  on weak turbulence of shear-Alfvén waves in the limit of strongly anisotropic pulsations that are elongated along a strong external magnetic field. The kinetic equation for energy is presented at the level of three-wave interactions. It is in agreement with the Galtier et al.  formulation of the full three-dimensional helical case when taking the proper limit. The simplified formalism induced by the new approach renders the applicability conditions for weak turbulence more transparent. It provides an attractive theoretical framework for describing anisotropic MHD turbulence in astrophysical contexts where a strong magnetic field is present and for which shear-Alfvén waves are important.