  We briefly review the current situation with various relations between
knot/braid polynomials (Chern-Simons correlation functions), ordinary and
extended, considered as functions of the representation and of the knot
topology. These include linear skein relations, quadratic Plucker relations, as
well as "differential" and (quantum) A-polynomial structures. We pay a special
attention to identity between the A-polynomial equations for knots and Baxter
equations for quantum relativistic integrable systems, related through
Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT
relation to the q-Virasoro algebra. This identity is an important ingredient of
emerging a 3d-5d generalization of the AGT relation. The shape of the Baxter
equation (including the values of coefficients) depend on the choice of the
knot/braid. Thus, like the case of KP integrability, where (some, so far torus)
knots parameterize particular points of the Universal Grassmannian, in this
relation they parameterize particular points in the moduli space of many-body
integrable systems of relativistic type.

High Energy Physics - Theory;Geometric Topology;Quantum Algebra