His research is in the fields of low-dimensional topology, representation theory, and quantum groups.

He and Vladimir Turaev constructed invariants of 3-manifolds which are expected to describe quantum Chern–Simons field theory introduced by Edward Witten.

He gave a plenary lecture at the International Congress of Mathematicians in 2010.

[1] He was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to the theory of quantum groups, integrable systems, topology, and quantum physics".

[2] In 2022, Reshetikhin received the inaugural Weyl-Wigner Award from ICGTMP.