ABSTRACT: The Severi degrees of P1XP1 can be computed in terms of an explicit operator on the Fock space F[P1]. We will discuss this approach and will also describe several further applications. We will discuss using Fock spaces to compute relative Gromov-Witten theory of other surfaces, such as Hirzebruch surfaces and EXP1. We will also discuss operators which calculate descendants. Joint with R. Pandharipande.