This article discusses the challenges that the ΛCDM cosmological model faces on small scales, specifically in the context of dark matter and galaxy formation. The ΛCDM model has been successful in explaining the large-scale structure of the universe and the evolution of galaxies. However, on scales smaller than about 1 Mpc and for dark matter halos with masses less than 10^11 solar masses, the model faces several problems. These include the observed cores of dark-matter dominated galaxies being less dense and less cuspy than predicted, the number of small galaxies and dwarf satellites in the Local Group being far below the predicted count of low-mass dark matter halos, and the presence of satellite planes and regularity in the galaxy population that are not well explained by ΛCDM. The article also discusses potential solutions to these challenges, including a better understanding of baryon physics, dark matter physics, or both. It highlights the importance of future surveys to discover faint, distant dwarf galaxies and to precisely measure their masses and density structure, as well as observational programs to constrain or discover the number of truly dark low-mass halos. The article concludes that these efforts will either further verify the ΛCDM paradigm or demand a substantial revision in our understanding of the nature of dark matter.This article discusses the challenges that the ΛCDM cosmological model faces on small scales, specifically in the context of dark matter and galaxy formation. The ΛCDM model has been successful in explaining the large-scale structure of the universe and the evolution of galaxies. However, on scales smaller than about 1 Mpc and for dark matter halos with masses less than 10^11 solar masses, the model faces several problems. These include the observed cores of dark-matter dominated galaxies being less dense and less cuspy than predicted, the number of small galaxies and dwarf satellites in the Local Group being far below the predicted count of low-mass dark matter halos, and the presence of satellite planes and regularity in the galaxy population that are not well explained by ΛCDM. The article also discusses potential solutions to these challenges, including a better understanding of baryon physics, dark matter physics, or both. It highlights the importance of future surveys to discover faint, distant dwarf galaxies and to precisely measure their masses and density structure, as well as observational programs to constrain or discover the number of truly dark low-mass halos. The article concludes that these efforts will either further verify the ΛCDM paradigm or demand a substantial revision in our understanding of the nature of dark matter.