Attention is focused on a suspension of buoyant particles (or droplets) in acontinuous fluid. In the presence of a force field, gravitational or centrifugal, and exposed to ordinary boundary constraints, a variety of fascinating flows can be obtained. These motions are essential ingre- dients in the widely used separation technology, where im- provedand new designs may be beneficial, but they are also interesting from a broader, academic point of view. In these respects, the recent investigations on these flows patterns, their underlying mechanisms and mathematical modeling - have accrued to a significant, relevant body of knowledge. The main objective of this book is to summarize - in a systematic, coherent and consistent fashion - the theoretical up to date contributions which seem fundamental in understanding, simulation and development of the subject.