Denis Perrot has pioneered a new approach to index cocycles in cyclic cohomology (Adv. Math., 2013) that has found siginificant applications. For instance Perrot and Rodsphon have used it to answer long-standing questions in the transverse index theory of Connes and Moscovici. I shall try to give an accessible introduction to Perrot’s method that emphasizes some of its geometric aspects. This is joint work with Jonathan Block and Jesus Sanchez.