The dwarf galaxy problem (aka missing satellite problem) is the discrepancy between the number of dwarf galaxies observed and of those showing up in cosmological simulations, specifically simulations based on cold dark matter (CDM), such as those based upon the Lambda-CDM model. The cosmological simulations produce significantly more dwarf galaxies than are observed, specifically satellite galaxies occurring at high-dark matter-density points within larger galaxies' dark matter halos. CDM models show advantages over competing theories but this weakness remains and variants and alternatives are put forward to resolve this issue while retaining the characteristics of CDM that work well. The problem also lends interest to discoveries of additional dwarf galaxies and techniques for identifying more of them: if enough additional such galaxies are discovered, the problem is resolved, and any update in galaxy demographics are significant to the evaluation of cosmological models and simulations.
One of the proposed solutions is that these dwarf satellite galaxies did exist but have been torn apart by interactions with the host galaxy by tidal forces (e.g., producing tidal tails of stars). This further theory has its own problem, termed the too-big-to-fail problem (TBTF), that some of the points at which satellite galaxies would seem to form have so much dark-matter mass that they ought to create galaxies too substantial to be obliterated.