In this talk, I hope to describe the state-of-the-art of the program of applying motivic integration to harmonic analysis on p-adic groups (which will be defined in the talk) that was started by T.C. Hales in 1999. In particular, I will talk about the recent joint work with R. Cluckers and I. Halupczok that allows to transfer results of very analytic flavour between fields of positive and zero characteristic, and prove uniform in p estimates for certain p-adic integrals, as p varies.