We report on recent results of the authors concerning calculations of quantum
invariants of Seifert 3–manifolds. These results include a derivation of the
Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated with an
arbitrary complex finite dimensional simple Lie algebra, and a determination of the
asymptotic expansions of these invariants for lens spaces. Our results are in
agreement with the asymptotic expansion conjecture due to J. E. Andersen.