  Our goal is to review the known theory on the one-dimensional obstacle
problem for the wave equation, and to discuss some extensions. We introduce the
setting established by Schatzman within which existence and uniqueness of
solutions can be proved, and we prove that (in some suitable systems of
coordinates) the Lipschitz norm is preserved after collision. As a consequence,
we deduce that solutions to the obstacle problem (both simple and double) for
the wave equation have bounded Lipschitz norm at all times. Finally, we discuss
the validity of an explicit formula for the solution that was found by
Bamberger and Schatzman.
