  The Problem of Time occurs because the `time' of GR and of ordinary Quantum
Theory are mutually incompatible notions. This is problematic in trying to
replace these two branches of physics with a single framework in situations in
which the conditions of both apply, e.g. in black holes or in the very early
universe. Emphasis in this Review is on the Problem of Time being multi-faceted
and on the nature of each of the eight principal facets. Namely, the Frozen
Formalism Problem, Configurational Relationalism Problem (formerly Sandwich
Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly
Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time,
Problem of Beables (alias Problem of Observables) and Spacetime
Reconstruction/Replacement Problem. Strategizing in this Review is not just
centred about the Frozen Formalism Problem facet, but rather about each of the
eight facets. Particular emphasis is placed upon A) relationalism as an
underpinning of the facets and as a selector of particular strategies
(especially a modification of Barbour relationalism, though also with some
consideration of Rovelli relationalism). B) Classifying approaches by the full
ordering in which they embrace constrain, quantize, find time/history and find
observables, rather than only by partial orderings such as "Dirac-quantize". C)
Foliation (in)dependence and Spacetime Reconstruction for a wide range of
physical theories, strategizing centred about the Problem of Beables, the
Patching Approach to the Global Problem of Time, and the role of the
question-types considered in physics. D) The Halliwell- and
Gambini-Porto-Pullin-type combined Strategies in the context of semiclassical
quantum cosmology.
