  We give a review of some recent work on generalization of the Bethe ansatz in
the case of $2+1$-dimensional models of quantum field theory. As such a model,
we consider one associated with the tetrahedron equation, i.e. the
$2+1$-dimensional generalization of the famous Yang--Baxter equation. We
construct some eigenstates of the transfer matrix of that model. There arise,
together with states composed of point-like particles analogous to those in the
usual $1+1$-dimensional Bethe ansatz, new string-like states and
string-particle hybrids.
