Irreversible aggregation sometimes leads to situations in which an infinite aggregate is formed in a finite time and in a way similar to what happens in percolation. In the mean-field approximation, the relevant description parameters of the aggregation process are the reaction rates between aggregates as functions of their respective masses. The main object of interest is the cluster size distribution, which gives the concentration of clusters of mass m at time t. The aim of scaling theory is to provide a simplified description of the cluster size distribution when t is very close to the critical time t_c at which the infinite cluster appears, and when m is very large. Such theories have been proposed since the eighties, but have clashed with numerical evidence. I shall discuss the reasons for this discrepancy, as well as recent attempts to resolve the issue.