  Smoluchowski's coagulation equation is a mean-field model describing the
growth of clusters by successive mergers. Since its derivation in 1916 it has
been studied by several authors, using deterministic and stochastic approaches,
with a blossoming of results in the last twenty years. In particular, the use
of weak $L^1$-compactness techniques led to a mature theory of weak solutions
and the purpose of these notes is to describe the results obtained so far in
that direction, as well as the mathematical tools used.
