In the first lecture I will present a survey of the history of problem of scaling limits for self-repelling random walks and diffusions. This will include the conjectures formulated in the mid-eighties and the existing mathematically rigorous results, proven between the mid nineties and recent months. In the second lecture I will concentrate on the technical details of two recent results.These are the CLT valid in three and more dimensions (joint work with I. Horvath and B. Veto, to appear in PTRF) and the superdiffusive bounds with logarithmic multiplivcative corrections valid in two dimensions (joint work with B. Valko, submitted). These results rely on Kipnis-Varadhan, respectively, Salmhofer-Landim-Quastel-Yau type arguments, involving graded (Gaussian) Hilbert space techniques.