  Attaining the limit of sub-microarcsecond optical resolution will completely
revolutionize fundamental astrometry by merging it with relativistic
gravitational physics. Beyond the sub-microarcsecond threshold, one will meet
in the sky a new population of physical phenomena caused by primordial
gravitational waves from early universe and/or different localized astronomical
sources, space-time topological defects, moving gravitational lenses, time
variability of gravitational fields of the solar system and binary stars, and
many others. Adequate physical interpretation of these yet undetectable
sub-microarcsecond phenomena can not be achieved on the ground of the
"standard" post-Newtonian approach (PNA), which is valid only in the near-zone
of astronomical objects having a time-dependent gravitational field. We
describe a new, post-Minkowskian relativistic approach for modeling astrometric
observations having sub-microarcsecond precision and briefly discuss the
light-propagation effects caused by gravitational waves and other phenomena
related to time-dependent gravitational fields. The domain of applicability of
the PNA in relativistic space astrometry is explicitly outlined.
