The satellite galaxies of the Milky Way and Andromeda preferentially co-orbit within narrow planes, and there is some evidence that satellite planes are also present around more distant hosts. Detailed comparisons show that similarly anisotropic phase-space distributions of sub-halos are extremely rare in cosmological simulations. This makes the satellite planes one of the most-serious small-scale problem for ΛCDM. In contrast to other small-scale problems, the satellite planes issue is not strongly affected by baryonic processes because the distribution of sub-halos on scales of hundreds of kpc is dominated by gravitational effects. While scenarios explaining the coherence of satellite positions and orbits exist, they all are currently unable to satisfactorily resolve the issue. To understand the existence and origin of the satellite planes, we have to move beyond a descriptive to a deductive use of the observed satellite correlations, and also consider additional, potentially related features and dwarf galaxy alignments in the Local Group.