Surfactant molecules (micelles) can self-assemble in solution into long flexible structures known as wormlike micelles. These structures entangle, forming a dense network and thus exhibit viscoelastic effects, similar to entangled polymer melts. In contrast to 'inert' polymeric networks, wormlike micelles continuously break and reform leading to an additional relaxation mechanism and the name 'living polymers.' Experimental studies show that, in shearing flows, wormlike micellar solutions exhibit spatial inhomogeneities, or shear bands. The VCM model, a two-species elastic network model was formulated to capture, in a self-consistent manner, the micellar breakage and reforming. This model consists of a coupled set of partial differential equations describing the breakage and reforming of two micellar species (a long species 'A' and a shorter species ‘B’) - in addition to reptative and Rousian stress-relaxation mechanisms. Transient and steady-state calculations of the full inhomogeneous flow field show localized shear bands that grow linearly in spatial extent across the gap as the apparent shear rate is incremented. This model also captures the non-monotonic variation in the steady state elongational viscosity that has been reported experimentally and the marked differences between the response of micellar solutions in biaxial and uniaxial extensional flows. The non-monotonic variation in the extensional viscosity has important dynamical consequences in transient elongational flows; In filament stretching experiments designed to measure the extensional rheology of wormlike micelle solutions, it has been observed that the elongating filaments may suddenly rupture near the axial mid-plane at high strain rates [Rothstein]. This newly-observed failure mechanism is not related to the visco-capillary thinning observed in viscous Newtonian fluids. Results of time-dependent simulations with the model carried out in a slender filament formulation appropriate for elongational flows of complex fluids are presented. The simulations show that elongating filaments described by the VCM model exhibit a dramatic and sudden rupture event similar to that observed in experiments. This instability is purely elastic in nature (i.e. it is not driven by capillarity) but arises from coupling between the evolution in the tensile stress and the number density of the entangled species. The dynamics of this localized necking are contrasted with predictions of other nonlinear viscoelastic models.