  A key problem in making precise perturbative QCD predictions is to set the
proper renormalization scale of the running coupling. The conventional
scale-setting procedure assigns an arbitrary range and an arbitrary systematic
error to fixed-order pQCD predictions. In fact, this {\it ad hoc} procedure
gives results which depend on the choice of the renormalization scheme, and it
is in conflict with the standard scale-setting procedure used in QED.
Predictions for physical results should be independent of the choice of scheme
or other theoretical conventions. We review current ideas and points of view on
how to deal with the renormalization scale ambiguity and show how to obtain
renormalization scheme- and scale- independent estimates. We begin by
introducing the renormalization group (RG) equation and an extended version,
which expresses the invariance of physical observables under both the
renormalization scheme and scale-parameter transformations. The RG equation
provides a convenient way for estimating the scheme- and scale- dependence of a
physical process. We then discuss self-consistency requirements of the RG
equations, such as reflexivity, symmetry, and transitivity, which must be
satisfied by a scale-setting method. Four typical scale setting methods
suggested in the literature, {\it i.e.,} the Fastest Apparent Convergence (FAC)
criterion, the Principle of Minimum Sensitivity (PMS), the
Brodsky-Lepage-Mackenzie method (BLM), and the Principle of Maximum
Conformality (PMC), are introduced. Basic properties and their applications are
discussed. We pay particular attention to the PMC, which satisfies all of the
requirements of RG invariance...... [full Abstract is in the paper].
