While definable types are usually studied in "tame" contexts, their usefulness and amenability to model-theoretic investigation even "in the wild" is, historically, not a surprise: for instance, Lascar defined the tensor product of definable types by generalising the existing notion on ultrafilters, which may be viewed as (trivially) definable types in the richest possible language on a given set. By pushing the tensor product forward along the addition, one shows that the usual sum of integers may be extended to the space of ultrafilters over Z, yielding a compact right topological semigroup. The analogous construction also goes through for the product, and these facts had important applications in additive combinatorics and Ramsey theory. Recently, B. ?obot introduced two (ternary) notions of congruence on the space above. I will talk about joint work with M. Di Nasso, L. Luperi Baglini, M. Pierobon and M. Ragosta, in which the study of these congruences led us to isolate a class of ultrafilters enjoying characterisations in terms of tensor products, directed sets, profinite groups, and more.