  This article contains a local solution to the notorious Problem of Time in
Quantum Gravity at the conceptual level and which is actually realizable for
the relational triangle. The Problem of Time is that `time' in GR and `time' in
ordinary quantum theory are mutually incompatible notions, which is problematic
in trying to put these two theories together to form a theory of Quantum
Gravity. Four frontiers to this resolution in full GR are identified, alongside
three further directions not yet conquered even for the relational triangle.
  This article is also the definitive review on relational particle models
originally due to Barbour (2003: dynamics of pure shape) and Barbour and
Bertotti (1982: dynamics of shape and scale). These are exhibited as useful toy
models of background independence, which I argue to be the `other half' of GR
to relativistic gravitation, as well as the originator of the Problem of Time
itself. Barbour's work and my localized extension of it are shown to be the
classical precursor of the background independence that then manifests itself
at the quantum level as the full-blown Problem of Time. In fact 7/8ths of the
Isham--Kuchar Problem of Time facets are already present in classical GR; even
classical mechanics in relational particle mechanics formulation exhibits
5/8ths of these! In addition to Isham, Kuchar and Barbour, the other principal
authors whose works are drawn upon in building this Problem of Time approach
are Kendall (relational models only: pure-shape configuration spaces), Dirac,
Teitelboim and Halliwell (Problem of Time resolving components). The
recommended scheme is a combination of the Machian semiclassical approach,
histories theory and records theory.
