I will present, in a concrete way, the formalism constructed for motivic exponential functions by F. Loeser and myself, and some new generalisations and variants of the transfer principle of the mentioned work. In the course of the talk, I give an overview of the presently known transfer principles in this context, some ideas of their proofs, and some of their applications in representation theory, being recent work with Julia Gordon and Immanuel Halupczok.