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Perturbation theory is one of the fundamental tool to study Quantum Mechanics and Quantum Field Theory, though it is known that the associated power series in the expansion parameter is mathematically ill-defined and not convergent in general. In certain cases it turns out that the series can be resummed to the exact result. After a brief review on old results, I will focus on more recent developments that allowed us to extend the class of theories where perturbation theory is resummable.