O. Gnedin: The formation of dwarf galaxies and small-scale problems of lambda-CDM
The Lambda-CDM cosmological model works very well in predicting large scale structure. It however predicts many more dwarf galaxies than are found. This is called the "missing satellite problem" and it is not just a few missing, but it should be ten times more.
The solution may be twofold: fist of all, only the more massive of satellite halos may be able to retain enough gas to form stars and thereby are seen by us. In addition, subhalos evaporate due to tidal forces, once they come close to "their" big galaxy. It has been known since long from studies of the Local Group that different types of dwarfs live at different radii from the large galaxies and there seems to be an evolutionary connection.
A new method of measuring the DM-halo of the Milky Way are hypervelocity stars that move at 500-1000 km/s with respect to us. They probably have been slingshotted by the black hole in the center of our galaxy. By following and calculating the paths of these stars, the shape of the DM-halo can be determined and according to CDM, it should be triaxial. This test will yield first results in a few years and it is a good test of predictions from lambda-cold-dark-matter cosmology, which is the widely accepted picture of our universe.