A nonlinear field theory of fracture mechanics is developed for crack propagation in paramagnetic and ferromagnetic materials from the global energy balance equation and the non-negative global dissipation requirement. The crack-front generalized -integral is equivalent to the generalized energy release rate serving as the thermodynamic driving force for crack propagation and also related to the generalized energy-momentum tensor in a way similar to the material force method. On the basis of the developed theory, the generalized energy release rate method, the generalized -integral method, and the extended essential work of fracture method are proposed for quasistatic and dynamic fracture characterization of magnetosensitive materials in the presence of magnetothermomechanical coupling and dissipative effects. The present work overcomes the drawbacks and limitations of conventional fracture mechanics and resolves the controversial issues on magnetoelastic fracture criterion. Especially, the crack-front generalized -integral has an odd dependence on the magnetic induction intensity factor for a Griffith-type crack in a magnetoelastic solid.