Driven by the increasingly complete observational knowledge of systems of satellite galaxies, mutual spatial alignments and relations in velocities among satellites belonging to a common host have become a productive field of research. The Planes of Satellite Galaxies issue is maybe the best-known type of such phase-space correlations. There is an ongoing, controversial debate on how much of a challenge observed, flattened distributions of apparently co-orbiting satellite galaxies pose for the ?CDM model of cosmology. With the fast expansion of proper motion measurements in recent years, largely driven by Gaia, other peculiar phase-space correlations have been uncovered among the satellites of the Milky Way. Concurrently, more complete observational samples of satellite galaxies around more distant hosts now enable us to expand the study such correlations to the Andromeda galaxy, Centaurus A, and beyond. In my talk, I will provide an introduction to this highly active field of research. I will review some of our recent results concerning planes of satellite galaxies, lopsided satellite galaxy systems, a potential “too-many-satellites” problem, and talk about how these (dis-)agree with cosmological expectations and other suggested formation scenarios.