  I survey the use of the Haag expansion as a technique to solve quantum field
theories. After an exposition of the asymptotic condition and the Haag
expansion, I report the results of applying the Haag expansion to several
quantum field theories, including galilean-invariant theories, matter at finite
temperature (using the BCS model of superconductivity as an illustrative
example), the Nambu--Jona-Lasinio model and the Schwinger model. I conclude
with the outlook for further development of this method.
