A number of approximate methods for modeling aggregation of particulate suspensions have been extended to simulate breakup as well and have been tested by comparison with rigorous solutions for conditions representative of most aggregation-fragmentation processes. The simplest methods, based on a geometric discretization with size ratio equal to two, can calculate satisfactorily the average values of the population for particularly well-conditioned situations only and, even in those cases, are not capable of predicting the shape of the particle size distribution. Therefore more complex methods are usually required, capable of using denser size discretization. The characteristics of these models and the guidelines for their choice are discussed in the paper, by considering their accuracy, ability to produce error estimates, ease of implementation and speed.