  Langmuir waves take place in a quasi-neutral plasma and are modeled by the
Zakharov system. The phenomenon of collapse, described by blowing up solutions
plays a central role in their dynamics. We present in this article a review of
the main mathematical properties of blowing up solutions. They include
conditions for blowup in finite or infinite time, description of self-similar
singular solutions and lower bounds for the rate of blowup of certain norms
associated to the solutions.
