Suppose that particles are randomly distributed in $R^d$, and undergo identical stochastic motion independently of each other.  The Smoluchowski process describes the fluctuations in the number of particles within an observation region over time.  The first part of the talk discusses probabilistic properties of the Smoluchowski processes, while the second part deals with their statistics. We consider two different models of the particle displacement process: the undeviated uniform motion (where a particle moves with a random constant velocity along a straight line) and the Brownian displacement. In the setting of the undeviated uniform motion, we study the problems of estimating the mean speed and the speed distribution, while for the Brownian displacement model the problem of estimating the diffusion coefficient is considered. In all these settings, we develop estimators with provable accuracy guarantees.