Free many-particle systems have relatively simple eigenstates.  Nevertheless, these states possess non-trivial entanglement properties which serve as points of orientation for the whole field.  In the talk, it will be shown how one can obtain them from the correlations in the state, how this leads to a statistical physics problem and what the nature of this problem is.  The resulting spectra, which contain the basic entanglement information, will be discussed for a number of cases and an outline of further topics will be given.