The problem of doing multiscale MHD simulations is an important one with impact on many areas such as astrophysics, plasma physics and space physics. Yet such simulations have remained difficult to do till recently. The reason stems from the fact that the MHD system of equations not just respects global conservation, which is difficult to impose on a composite mesh, but it also satisfies additional constraints, the principal one being the divergence-free constraint. While those constraints are easy to satisfy on a uniform mesh they are difficult to satisfy on a hierarchical mesh. Recently the author made several advances in the divergence-free representation of vector fields. The advances include a comprehensive process of evolving such vector fields on hierarchical meshes with efficient timestep sub cycling on finer meshes. The advances have now been shown to extend to different meshes with complex geometry. One of the principal bonuses that arise is that the study makes it possible for us to have logically precise formulations for numerical MHD which overcome a lot of the shortcomings of previous methods. The MHD system serves as a prototype for other more complex systems too and all such systems would benefit from the advances reported in this talk.