As the top panel of Fig. 3 shows, ΛCDM predicts that there are many fairly massive subhalos within dark matter halos of galaxies like the Milky Way and the Andromeda galaxy, more than there are observed satellite galaxies Klypin et al. (1999), Moore et al. (1999). This is not obviously a problem for the theory since reionization, stellar feedback, and other phenomena are likely to suppress gas content and star formation in low-mass satellites. As more faint satellite galaxies have been discovered, especially using multicolor information from SDSS observations, the discrepancy between the predicted and observed satellite population has been alleviated. Many additional satellite galaxies are predicted to be discovered by deeper surveys (e.g., Bullock et al. (2010)), including those in the Southern Hemisphere seen by the Dark Energy Survey The DES Collaboration et al. (2015) and eventually the Large Synoptic Survey Telescope (LSST).
However, a potential discrepancy between theory and observations is the "too big to fail" (TBTF) problem Boylan-Kolchin et al. (2011), Boylan-Kolchin et al. (2012). The Via Lactea-II high-resolution dark-matter-only simulation of a Milky Way size halo Diemand et al. (2007), Diemand et al. (2008) and the six similar Aquarius simulations Springel et al. (2008) all have several subhalos that are too dense in their centers to host any observed Milky Way satellite galaxy. The brightest observed dwarf spheroidal (dSph)satellites all have 12 ≲ Vmax ≲ 25 km/s. But the Aquarius simulations predict at least 10 subhalos with Vmax > 25 km/s. These halos are also among the most massive at early times, and thus are not expected to have had their star formation greatly suppressed by reionization. They thus appear to be too big to fail to become observable satellites Boylan-Kolchin et al. (2012).
The TBTF problem is closely related to the cusp-core issue, since TBTF is alleviated by any process that lowers the central density and thus the internal velocity of satellite galaxies. Many of the papers finding that baryonic effects remove central cusps cited in the previous section are thus also arguments against TBTF. A recent simulation of regions like the Local Group found the number, internal velocities, and distribution of the satellite galaxies to be very comparable with observations Sawala et al. (2014).
Perhaps there is additional physics beyond ΛCDM that comes into play on small scales. One possibility that has been investigated is warm dark matter (WDM). A simulation like Aquarius but with WDM has fewer high-Vmax halos Lovell et al. (2012). But it is not clear that such WDM simulations with the lowest WDM particle mass allowed by the Lyman alpha forest and other observations Viel et al. (2013), Horiuchi et al. (2014) will have enough substructure to account for the observed faint satellite galaxies (e.g., Polisensky and Ricotti (2011)), and as already mentioned WDM does not appear to be consistent with observed systematics of small galaxies.
Another possibility is that the dark matter particles interact with themselves much more strongly than they interact with ordinary matter Spergel and Steinhardt (2000). There are strong constraints on such self-interacting dark matter (SIDM) from colliding galaxy clusters Harvey et al. (2015), Massey et al. (2015), and in hydrodynamic simulations of dwarf galaxies SIDM has similar central cusps to CDM Bastidas Fry et al. (2015). SIDM can be velocity-dependent, at the cost of adding additional parameters, and if the self-interaction grows with an inverse power of velocity the effects can be strong in dwarf galaxies Elbert et al. (2014). An Aquarius-type simulation but with velocity-dependent SIDM produced subhalos with inner density structure that may be compatible with the bright dSph satellites of the Milky Way Vogelsberger et al. (2012). Whether higher-resolution simulations of this type will turn out to be consistent with observations remains to be seen.