Individual particles suspended in a fluid collide by various mechanisms such as random Brownian motion of particles, differential settling velocities, flow turbulence and by differential velocity gradients in laminar flow. Among these mechanisms, coagulation due to Brownian motion is an important particle growth mechanism in situations where small aerosol particles at a high concentration (as in flame reactors) or long-term behavior of suspended particles (as in the atmosphere) are concerned. In this paper the dynamical aerosol process - Brownian coagulation - is reviewed. The most often used formulas for describing the collision rate over the entire particle size regime are presented in a general form. Numerical modeling techniques used to describe the changes of the size distribution due to the coagulation process are described and discussed. Available analytical solutions are summarized.