Hydrodynamical simulations played an important role in understanding the dynamics and shaping of planetary nebulae in the past century. However, hydrodynamical simulations were just a first order approach. The new millennium arrived with the generalized understanding that the effects of magnetic fields were necessary to study the dynamics of planetary nebulae. Thus, B-fields introduced a whole new number of physical possibilities for the modeling. In this paper, we review observational work done in the last 5 years and several works on the magnetohydrodynamics of proto-planetary nebulae, since all the effort has been focused on that stage, and discuss different scenarios for the origin of magnetized winds, and the binary-bipolarity relation.