  In this thesis we explore the physics of renormalons in integrable models
under the framework of resurgence. In the first part, we review some background
on resurgence, integrability and renormalons, including a discussion of large N
renormalons and ring diagrams. In the second part, we start from the Bethe
ansatz integral equations and obtain exact trans-series for the free energy in
multiple models. These trans-series include non-perturbative effects which
correspond to renormalons at unexpected positions in the Borel plane. We test
the trans-series numerically and at large N. We also study what happens to
these trans-series under a topological angle. In the third part, we use apply
the techniques of resurgence in non-relativistic theories. We find a relation
between the energy gap of the system and the positions of singularities in the
Borel plane. By studying the asymptotic behaviour of ring diagrams, we identify
this relation with renormalons.
