  The Cold Dark Matter model describes successfully our Universe on large
scales, as has been verified by a wide range of observations. Nevertheless, in
the last years, and especially with the advances in numerical simulations, a
number of apparent inconsistencies arose between what is observed and what the
CDM model predicts on small scales. In this work, the current status of
observations on galactic and subgalactic scales is reviewed. Furthermore,
theory and observation are brought together in order to reveal the nature of
the inconsistencies and, consequently, to reveal their severity. Lastly, the
progress towards the resolution of each one of these conflicts is briefly
reviewed.
