These notes put together a number of theoretical and numerical models and results obtained for magnetically soft and hard magnetorheological elastomers, denoted as s-MREs and h-MREs, respectively over the last five years in our group. We present in a unified manner both sand h-MREs. In particular, we regard MREs, in the general case, as magnetically dissipative nonlinear elastic composite materials comprising a mechanically-soft, non-magnetic elastomeric matrix in which mechanically-rigid, magnetically-dissipative particles are embedded isotropically and randomly. The proposed incremental variational frameworks are general enough to deal with more complex microstructures such as particle-chains or others that do not yet exist in the lab. More importantly, we propose homogenization-guided, analytical, explicit models that are consistent as one moves from the dissipative h-MREs to the purely energetic s-MREs. In parallel, we propose numerical frameworks allowing to simulate a very wide variety of microstructures and boundary value problems in magneto-mechanics.