  Floer field theory is a construction principle for e.g. 3-manifold invariants
via decomposition in a bordism category and a functor to the symplectic
category, and is conjectured to have natural 4-dimensional extensions. This
survey provides an introduction to the categorical language for the
construction and extension principles and provides the basic intuition for two
gauge theoretic examples which conceptually frame Atiyah-Floer type conjectures
in Donaldson theory as well as the relations of Heegaard Floer homology to
Seiberg-Witten theory.
