  We undertake a systematic review of some results concerning local
well-posedness of the Cauchy problem for certain systems of nonlinear wave
equations, with minimal regularity assumptions on the initial data. Moreover we
provide a considerably simplified and unified treatment of these results and
provide also complete proofs for large data. The paper is also intended as an
introduction to and survey of current research in the very active area of
nonlinear wave equations. The key ingredients throughout the survey are the use
of the null structure of the equations we consider and, intimately tied to it,
bilinear estimates.
