Abstract: "The goal of this talk is to report on the progress in the program of comparing the model of $(\infty,n)$-categories given by complicial sets with the more established models, in particular with cellular models. This is partially work in progress with Martina Rovelli, as well as previous work joint with Julie Bergner and Martina Rovelli. The plan for the talk is to explain all the terms of the first sentence, and then to go into details, time permitting"