The article summarizes the principal details of a method of moments with interpolative closure. This is a mathematically rigorous yet numerically economical approach to particle dynamics, describing time evolution of a particle ensemble undergoing simultaneous nucleation, coagulation, and surface growth. The method was introduced some time ago and since then has undergone further development as well as extensive testing in reactive flow simulations of practical systems. These results, scattered over quite diverse literature, are presented here in a unified form, focussing on logical development rather than on chronological order. In addition, the validity of the numerical approach is addressed on rigorous mathematical grounds. Also discussed are method shortcomings along with possible directions to their resolution.