  This is a survey of a new type of relativistic space-time framework; the
so-called quasi-metric framework. The basic geometric structure underlying
quasi-metric relativity is quasi-metric space-time; this is defined as a
4-dimensional differentiable manifold ${\cal N}$ equipped with two
one-parameter families ${\bf {\bar g}}_t$ and ${\bf g}_t$ of Lorentzian
4-metrics parametrized by a global time function $t$. The metric family ${\bf
{\bar g}}_t$ is found from field equations, whereas the metric family ${\bf
g}_t$ is used to propagate sources and to compare predictions to experiments. A
linear and symmetric affine connection compatible with the family ${\bf g}_t$
is defined, giving rise to equations of motion.
  Furthermore a quasi-metric theory of gravity, including field equations and
local conservation laws, is presented. Just as for General Relativity, the
field equations accommodate two independent propagating dynamical degrees of
freedom. On the other hand, the particular structure of quasi-metric geometry
allows only a partial coupling of space-time geometry to the active
stress-energy tensor. Besides, the field equations are defined from projections
of physical and geometrical tensors with respect to a "preferred" foliation of
quasi-metric space-time into spatial hypersurfaces. Moreover, a number of
non-standard features make the field equations unsuitable for a standard
PPN-analysis. This implies that the experimental status of the theory is not
completely clear at this point in time. The theory seems to be consistent with
a number of cosmological observations and it satisfies all the classical solar
system tests, though. In additon, in its non-metric sector, the new theory has
experimental support where General Relativity fails or is irrelevant.
