Abstract: Chern characters are natural transformations from K-theory like coarse homology theories to coarse homology theories derived from chain-complex constructions. Transgressions are natural transformations from coarse homology theories to functors applied to the Higson corona. I will explain instances of such constructions and how they are possibly related. One goal of this talk is to highlight the richness of the world of coarse homology theories and its connection with interesting developments, classical and modern, in other fields.