  This is a doctoral thesis dissertation developed in the frame of theoretical
QCD predictions, with focus on two main topics. On the one hand, the
large-order bahavior of perturbative QCD series is discussed. By reviewing the
main literature, a cohesive discussion is made that includes the topics of
large-order divergencies in QCD, renormalons, summation methods for asymptotic
series and non-perturbative power corrections. A formalism for perturbative QCD
series in the large-$\beta_0$ is presented, which allows for (1) the
computation of the series, its renormalization factor and anomalous dimension,
(2) the sum of all these quantities, (3) the study of the renormalon structure
of the series and (4), the ambiguity in the sum due to IR renormalons, which is
associated with the size of non-power corrections. Original and published work
has been made to develop this formalism for both series without and with
cusp-anomalous dimension. A large number of applications of our formalism are
also presented, covering the short-distance mass schemes $\bar{\rm MS}$ and
MSR, the QCD-to-SCET and SCET-to-bHQET matching coeficients and the SCET and
bHQET jet functions. On the other hand, original and also published work in
fixed-order perturbation theory is also carried out in the field of event
shapes. The event-shape distribution for $e^+e^-$ to hadrons is computed to NLO
differential with respect to the angle between the initial beam and the thrust
axis of the event. The relevant finding is the presence of the quark mass
already at $\cal{O}(\alpha_s^0)$ for the vector current. Finally, the
dissertation also contains a brief study on the FOPT-CIPT difference in the
context of tau decays.
