I will give a survey of the "lambda-SAW" viewpoint to SLE in terms of random walk (Brownian) loop measures.
Although convergence of the discrete model to the continuous is still very open (except in some cases), the perspective
gives intuition of how to approach questions like SLE in multiply connected domains and multiple paths.
I will also discuss some recent work with Mohammad Jahangoshahi and Vivian
Healey in this area.