Magnetic field relaxation in a plasma of very low density is considered, first in terms of a simple one-dimensional model in which the formation of current sheets can be explicitly realised. The buildup of fluid density at the location of the current sheets is very marked. Azimuthal field relaxation in a cylindrical annulus leading to the ‘pinch effect’ is then considered, and a similarity solution for current collapse in an unbounded fluid is obtained. Relaxation of a helical field and Taylor’s conjecture leading to a ‘Taylor state’ of prescribed global helicity is presented, with application to the reversed field pinch. The mechanism by which a reversed field can appear during the relaxation process is then considered; on the assumption that helical turbulence resulting from instabilities of the collapsing field is in some way responsible, an α-effect is incorporated in the relaxation process. It is shown that this can induce negative diffusivity and violent axial field instability near the cylinder boundary, with the tentative conclusion that an α-effect may indeed provoke axial field reversal near the boundary. Eruption and relaxation of twisted flux ropes in the solar corona are briefly considered.