The operator product expansion (OPE) is an important concept in particle physics and beyond. Within this framework physical observables can be expressed as a sum of expectation values of local operators that encode long distance physics, accompanied by short distance Wilson coefficients. The latter can, e.g., be computed in perturbation theory. The general mathematical structure is that of a trans-series. One example is the factorization within heavy quark effective theory (HQET) of a heavy-light meson mass into a heavy quark mass and a non-perturbative binding energy.

Coefficients of perturbative expansions usually diverge factorially. These divergencies can be related to singularities in the Borel plane. The so-called "renormalon" is a particular type of singularity that appears within Wilson coefficients of an OPE. I will discuss the theoretical background, show examples of such expansions for the self-energy of HQET and the action density of quantum chromodunamics. I will compare the coefficients to theoretical expectations and comment on implications for the definition of heavy quark masses and the non-perturbative gluon condensate.