The study of the large order behavior of infinite power series in QCD, which are the fundamental objects in perturbation theory, is adressed in the context of the large-b0 limit. A systematic formalism to extract closed expressions and renormalons is developed for regular series and extended to series with cusp anomalous dimension for the first time. A number of applications, such as short-distance mass-schemes and SCET and bHQET factorization theorems for dijets are considered in detail. The problem of asymptotic separation in the tau spectral moments is studied for the gluon-condensate Borel model, and the differences between the FOPT (convergent) and CIPT (divergent) schemes are clearly stablished. The fixed-order NLO computation of the event-shape distribution of e^+e^ to hadrons is presented for massive event-shapes and with explicit orientation of the thrust axis.
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