For several models of self-interacting random walks (SIRWs), generalized Ray-Knight theorems for edge local times are a very useful tool for studying the limiting distributions of these walks. Examples include some reinforced random walks, excited random walks, rotor walks with defects. I shall describe two classes of SIRWs studied by Balint Toth (1996), asymptotically free and polynomially self-repelling SIRWs, and discuss recent results (joint work with Thomas Mountford, EPFL, and Jon Peterson, Purdue University) which resolve an open question posed in Toth’s paper. We show that, in the asymptotically free case, the rescaled SIRWs converge to a perturbed Brownian motion (conjectured by Toth), while in the polynomially self-repelling case, the convergence to the conjectured process fails in spite of the fact that generalized Ray-Knight theorems clearly identify the unique candidate in the class of perturbed Brownian motions. This negative result was somewhat unexpected. Conjectures on whether there is a suitable limiting process in this case and, if yes, what it might be are welcome.