  The scaling theory of irreversible aggregation is discussed in some detail.
First, we review the general theory in the simplest case of binary reactions.
We then extend consideration to ternary reactions, multispecies aggregation,
inhomogeneous situations with arbitrary size dependent diffusion constants as
well as arbitrary production terms. A precise formulation of the scaling
hypothesis is given as well as a general theory of crossover phenomena. The
consequences of this definition are described at length. The specific issues
arising in the case in which an infinite cluster forms at finite times (the
so-called gelling case) are discussed, in order to address discrepancies
between theory and recent numerical work. Finally, a large number of exactly
solved models are reviewed extensively with a view to pointing out precisely in
which sense the scaling hypothesis holds in these various models. It is shown
that the specific definition given here will give good results for almost all
cases. On the other hand, we show that it is usually possible to find
counterexamples to stronger formulations of the scaling hypothesis.
