  We discuss the Hartree equation arising in the mean-field limit of large
systems of bosons and explain its importance within the class of nonlinear
Schroedinger equations. Of special interest to us is the Hartree equation with
focusing nonlinearity (attractive two-body interactions). Rigorous results for
the Hartree equation are presented concerning: 1) its derivation from the
quantum theory of large systems of bosons, 2) existence and stability of
Hartree solitons, and 3) its point-particle (Newtonian) limit. Some open
problems are described.
