  The conventional spacetime formulation of general relativity may be recast as
a dynamics of spatial 3-geometries (geometrodynamics). Furthermore,
geometrodynamics can be derived from first principles. I investigate two
distinct sets of these: (i) Hojman, Kucha\v{r} and Teitelboim's, which
presuppose that the spatial 3-geometries are embedded in spacetime. (ii) The
3-space approach of Barbour, Foster, \'{O} Murchadha and Anderson in which the
spatial 3-geometries are presupposed but spacetime is not. I consider how the
constituent postulates of the conventional approach to relativity emerge or are
to be built into these formulations. I argue that the 3-space approach is a
viable description of classical physics (fundamental matter fields included),
and one which affords considerable philosophical insight because of its
`relationalist' character. From these assumptions of less structure, it is also
interesting that conventional relativity can be recovered (albeit as one of
several options).
  However, contrary to speculation in the earlier 3-space approach papers, I
also argue that this approach is not selective over which sorts of fundamental
matter physics it admits. In particular, it does not imply the equivalence
principle.
