  This thesis studies the role of free fermions in certain classical and
quantum integrable models. The classical models studied are the KP and BKP
hierarchies of partial differential equations. We review the presence of free
fermions in the theory of these hierarchies, a topic which was established in
the work of the Kyoto school. The quantum models studied are descendents and
relatives of the XYZ model, or its lattice equivalent, the eight-vertex model.
We give a number of new results in the context of these models, revealing the
presence of fermions in typical quantities such as Bethe eigenvectors,
partition functions and scalar products.
