  In this expository paper we present an overview of various graphical
categorifications of the Heisenberg algebra and its Fock space representation.
We begin with a discussion of "weak" categorifications via modules for Hecke
algebras and "geometrizations" in terms of the cohomology of the Hilbert
scheme. We then turn our attention to more recent "strong" categorifications
involving planar diagrammatics and derived categories of coherent sheaves on
Hilbert schemes.
