A number of observations of dwarf galaxies pose challenges to our understanding of the clustering of matter on small scales in the current ΛCDM paradigm. These include the scarcity of dwarf galaxies compared with the numerous low-mass halos expected in the current ΛCDM paradigm (the 'missing satellites‘ problem); the inner mass profiles of cold dark matter halos compared with the rotation curves of dwarf galaxies (the ΄cusp vs core‘ problem); the highly anisotropic distribution of satellite galaxies around the Milky Way and Andromeda galaxies (the ΄satellite alignment‘ problem); and the low halo masses inferred for the faintest dwarfs (the ΄too-big-to-fail‘ problem). I will discuss these challenges, as well as the puzzles and challenges that arise from them and from their possible resolution.