The eigenerosion approach has been proposed in [1] as a particular application of the more general eigendeformation method [2]. The approach has been developed to overcome the issues related to the propagation of cracks within a discretized solid body. A discretization, either in finite elements or in particles, automatically introduces a bias into the solid, and creates preferential paths for a propagating crack. Thus, methods that describe advancing cracks in finite element models are affected by mesh dependency (see traditional cohesive elements) or require heavy coding to introduce intra-element cracks (XFEM). In the spirit of the very popular phase field methods, eigenfracture (and eigenerosion) alleviate the difficulty to model a set of cracks seen as they actually are, i.e., surfaces, by regularizing them over a surrounding volume. In contrast to phase field, that introduces an additional field to model the progressive reduction of the elastic energy according to a complex function of the distance from the crack, eigenerosion introduces a length scale (larger than the mesh size) to define a crack neighborhood. The neighborhood elements are released from their elastic energy and they do not contribute anymore to the crack advance and to the mechanical stiffness of the solid. The auxiliary length scale makes the method mesh independent, and no mesh refinement is necessary to capture the global response of the system. Eigenerosion has been successfully applied to model brittle and ductile fracture in solids discretized in finite elements or in material points, and extensions are under study to include coupling to other phenomena in order to describe rupture in biological tissues.