  In this chapter we review recent results concerning localized and extended
dissipative solutions of the discrete complex Ginzburg-Landau equation. In
particular, we discuss discrete diffraction effects arising both from linear
and nonlinear properties, the existence of self-localized dissipative solitons
in the presence of cubic-quintic terms and modulational instability induced by
saturable nonlinearities. Dynamical stability properties of localized and
extended dissipative discrete solitons are also discussed.
