Satellite galaxies of the Milky Way and of the Andromeda galaxy have been found to preferentially align in significantly flattened planes of satellite galaxies, and available velocity measurements are indicative of a preference of satellites in those structures to co-orbit. There is increasing evidence that such kinematically correlated satellite planes are also present around more distant hosts. Detailed comparisons show that similarly anisotropic phase-space distributions of sub-halos are exceedingly rare in cosmological simulations based on the ΛCDM paradigm. Analogs to the observed systems have frequencies of ≤ 0.5 per cent in such simulations. 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. This makes the satellite planes one of the most serious small-scale problem for ΛCDM. This review summarizes the observational evidence for planes of satellite galaxies in the Local Group and beyond, and provides an overview of how they compare to cosmological simulations. It also discusses scenarios which aim at explaining the coherence of satellite positions and orbits, and why they all are currently unable to satisfactorily resolve the issue. 1:17 WSPC/INSTRUCTION FILE review 2 Marcel S. Pawlowski successes do not constitute proof of correctness, 2, 3 and science strives to probe the limitations of its models by pushing to test them in novel ways. In particular when expanded beyond its initial scope of applicability, a model is most thoroughly tested and opportunities for refinement or revision can be identified. For ΛCDM -developed to fit the large-scale structure and evolution of the Universe (on scales of many Mpc to Gpc) -such a novel domain of applicability is the regime of galaxies and their satellite galaxy systems (on scales of hundreds of kpc and below). Due to the non-linearity of ΛCDM on those scales, model predictions are made via numerical simulations. These evolve an initially almost homogenious matter distribution forward in time, simulating the formation and evolution of structure in the cosmos until the present day. This implies an important caveat for tests in this regime: not the model itself is tested directly, but its realisation via numerical simulations.Our best observational knowledge of the smallest galaxies stems from observation of the ≈ 50 and 40 known dwarf Spheroidal (dSph) satellite galaxies of our Milky Way (MW) and the neighboring Andromeda galaxy (M31), respectively. Together with ≈ 15 more isolated dwarf galaxies, they make up the Local Group of galaxies, covering a volume of approximately 1 Mpc in radius. Comparisons of cosmological simulations of dark matter halos resembling those expected to host the MW and M31 with the observed systems have revealed a number of small-scale problems of ΛCDM. 4 Among the best known issues are the Missing Satellites Problem, the Core-Cusp Problem, and the Too-Big-to-Fail problem...