Rational, trigonometric, elliptic algebras and moduli spaces of sheaves on surfaces

We survey the well-known Yangian of ${\widehat{\mathfrak{g}\mathfrak{l}}}_1$ /quantum toroidal ${\mathfrak{g}\mathfrak{l}}_1$ action on the cohomology / $K$-theory of moduli spaces of stable sheaves on surfaces, and give the generalization of this construction to elliptic cohomology.