The Lambda Cold Dark Matter model is well established as the framework within which we study the origin and growth of structure in the Universe from the earliest cosmic epoch to the present day. Yet a recurring theme for the LCDM model over the last two decades has been that it faces a crisis on small-scales, predicting an overabundance of low-mass galaxies whereas comparatively few are observed. Can this tension be explained by appealing to known astrophysical processes, or does it signal the need for a fundamental overhaul of the dark matter model itself? I will review the current state of affairs, highlighting where our theoretical understanding needs to be improved, and I will discuss the kind of observations that might help us test dark matter models in the most robust fashion.