Survey of exactly solved models for conducting polymers

We present an overview of one-dimensional interacting quantum many-body systems that have been solved exactly over the last 60 years. Our attention is drawn to three models which are most relevant for conducting polymers: the Heisenberg-Ising spin chain, the Hubbard model and the sinh-cosh model. The emphasis of this tutorial will be on theoretical models — but not theory! — rather than applications to particular experiments or polymers.