  This is partly an expository paper, where the authors' work on
pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new
criterion is given for the existence of a diagonal Einstein metric on a nice
nilpotent Lie group. Classifications of special classes of Ricci-flat metrics
on nilpotent Lie groups of dimension $\leq8$ are obtained. Some related open
questions are presented.
