  We provide a classification and an explicit realization of all irreducible
Gelfand-Tsetlin modules of the complex Lie algebra sl(3). The realization of
these modules uses regular and derivative Gelfand-Tsetlin tableaux. In
particular, we list all simple Gelfand-Tsetlin sl(3)-modules with
infinite-dimensional weight spaces. Also, we express all simple Gelfand-Tsetlin
sl(3)-modules as subquotionets of localized Gelfand-Tsetlin E_{21}-injective
modules.
