k3 surfaces are two dimensional calabi-yau manifolds. their moduli space is of interest in algebraic geometry, but also has connections with number theory and string theory. i will discuss ongoing joint work with alina marian and rahul pandharipande aimed at studying the tautological ring of the moduli space of k3 surfaces. in particular, i will discuss different notions of tautological classes. next, i will explain a method of deriving relations between tautological classes via the geometry of the relative quot scheme.