  Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite
number of microscopic constraints expressing mass, entropy and magnetic flux
conservation in each infinitesimal fluid element, the latter preventing
magnetic reconnection. By contrast, in the Taylor relaxation model for
formation of macroscopically self-organized plasma equilibrium states, all
these constraints are relaxed save for global magnetic fluxes and helicity. A
Lagrangian variational principle is presented that leads to a new, fully
dynamical, \emph{relaxed magnetohydrodynamics} (RxMHD), such that all static
solutions are Taylor states but also allows flow. By postulating that some
long-lived macroscopic current sheets can act as barriers to relaxation,
separating the plasma into multiple relaxation regions, a further
generalization, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is
developed.
