Magnetic shape-memory alloys owe their exceptional properties primarily to the accompanying effects of a martensitic phase transformation. The twinning disconnection as elementary carrier of magnetic-field-induced deformation is the starting point of the present study. A disconnection is a line defect similar to a dislocation but located at an interface and exhibiting a step character besides a dislocation character. The mutual interaction of disconnections is fully tractable by the theory of dislocations. Due to the martensitic transformation, a hierarchical twin microstructure evolves, details of which are controlled through disconnection-disconnection interaction. Depending on the mutual orientation of twin boundaries on different hierarchical levels, twinning disconnections are incorporated in higher hierarchical twin boundaries forming disclination walls, or they stand off individually from those interfaces. Disconnections which stand off from interfaces contribute to magnetoelasticity, i.e. recoverable magnetic-field-induced deformation. Disconnections in disclination walls contribute to magnetoplasticity, i.e. permanent magnetic-field-induced deformation, if the twin thickness is large. In self-accommodated martensite with very thin twins, resulting from a martensitic transformation without training, the deformation is fully magnetoelastic and small. In single-domain crystals, resulting from effective thermo-magnetomechanical training, the deformation is fully magnetoplastic and large. Between these limiting cases, there is a continuous spectrum where, as a rule, the fraction of magnetoplastic strain and the total strain increase with increasing effectiveness of training.