  We describe results concerning the existence proofs of Discrete Breathers
(DBs) in the two classes of dynamical systems with optical linear phonons and
with acoustic linear phonons. A standard approach is by continuation of DBs
from an anticontinuous limit. A new approach, which is purely variational, is
presented. We also review some numerical results on intraband DBs in random
nonlinear systems. Some non-conventional physical applications of DBs are
suggested. One of them is understanding slow relaxation properties of glassy
materials. Another one concerns energy focusing and transport in biomolecules
by targeted energy transfer of DBs. A similar theory could be used for
describing targeted charge transfer of nonlinear electrons (polarons) and, more
generally, for targeted transfer of several excitations (e.g. Davydov soliton).
