  This is a review paper on the Gelfand-Tsetlin type bases for representations
of the classical Lie algebras. Different approaches to construct the original
Gelfand-Tsetlin bases for representations of the general linear Lie algebra are
discussed. Weight basis constructions for representations of the orthogonal and
symplectic Lie algebras are reviewed. These rely on the representation theory
of the B,C,D type twisted Yangians
