Population balance models have been used in chemical engineering since the 1960s and have evolved to become the most important tools for design and control of particulate processes. In this paper we show that the intrinsic particle parameter that determines changes in the process and should thus be included in the population balance is the particle volume. The basic population that is modeled should be the mass distribution, or the volume distribution if the density is constant. The population balance thus describes the change of the volume distribution of volume with time. Furthermore, we suggest that the "birth" and "death" terms that are often used to describe discrete events in particulate processes can almost always be replaced by a rate of change term. To design and control existing and future processes, a multi-dimensional population balance model is required. We propose a volume-based model in which the particle properties that are modeled are the volumes of solid, liquid, and air, respectively. In the most general case the model will consist of a properties vector and a distribution tensor. Depending on the complexity of the process, one or more of the properties may be omitted from the model. This is shown in three examples of increasing complexity: comminution, sintering, and granulation.