  A key issue in making precise predictions in QCD is the uncertainty in
setting the renormalization scale $\mu_R$ and thus determining the correct
values of the QCD running coupling $\alpha_s(\mu_R^2)$ at each order in the
perturbative expansion of a QCD observable. It has often been conventional to
simply set the renormalization scale to the typical scale of the process $Q$
and vary it in the range $\mu_R \in [Q/2,2Q]$ in order to estimate the
theoretical error. This is the practice of Conventional Scale Setting (CSS).
The resulting CSS prediction will however depend on the theorist's choice of
renormalization scheme and the resulting pQCD series will diverge factorially.
It will also disagree with renormalization scale setting used in QED and
electroweak theory thus precluding grand unification. A solution to the
renormalization scale-setting problem is offered by the Principle of Maximum
Conformality (PMC), which provides a systematic way to eliminate the
renormalization scale-and-scheme dependence in perturbative calculations. The
PMC method has rigorous theoretical foundations, it satisfies Renormalization
Group Invariance (RGI) and preserves all self-consistency conditions derived
from the renormalization group. The PMC cancels the renormalon growth, reduces
to the Gell-Mann--Low scheme in the $N_C\to 0$ Abelian limit and leads to
scale- and scheme-invariant results. The PMC has now been successfully applied
to many high-energy processes. In this article we summarize recent developments
and results in solving the renormalization scale and scheme ambiguities in
perturbative QCD. [full abstract is in the paper].
