  This paper provides an introduction to exploded manifolds. The category of
exploded manifolds is an extension of the category of smooth manifolds with an
excellent holomorphic curve theory. Each exploded manifold has a tropical part
which is a union of convex polytopes glued along faces. Exploded manifolds are
useful for defining and computing Gromov-Witten invariants relative to normal
crossing divisors, and using tropical curve counts to compute Gromov-Witten
invariants.
