  Extragalactic proper motions can reveal a variety of cosmological and local
phenomena over a range of angular scales. These include observer-induced proper
motions, such as the secular aberration drift caused by the solar acceleration
about the Galactic Center and a secular extragalactic parallax resulting from
our motion with respect to the cosmic microwave background rest frame.
Cosmological effects include anisotropic expansion, transverse peculiar
velocities induced by large scale structure, and the real-time evolution of the
baryon acoustic oscillation. Long-period gravitational waves can deflect light
rays, producing an apparent quadrupolar proper motion signal. We review these
effects, their imprints on global correlated extragalactic proper motions,
their expected amplitudes, the current best measurements (if any), and
predictions for Gaia. Finally, we describe a possible long-baseline ngVLA
program to measure or constrain these proper motion signals. In most cases, the
ngVLA can surpass or complement the expected end-of-mission performance of the
Gaia mission.
