Two and three-phase flow processes involving gas, liquid and solid, are common in nature and industry, and include some of the most complex and poorly-understood transport problems. In this research hydrodynamics, heat and mass transfer processes in complex two and three-phase flows were investigated. The interfacial surface area concentration in a short vertical column subject to the through flow of fiber-liquid-gas slurry was experimentally measured using the gas absorption technique. The experimental data were statistically analyzed for parametric effects, and were empirically correlated. The absorption of a gaseous species by a slurry droplet with internal circulation and containing reactive micro-particles was simulated, and parametrically studied. The micro-particles were found to enhance the absorption rate. The absorption rate was sensitive to droplet recirculation, and shrinkage of particles with time resulted in declining absorption rates. The transport of soot particles, suspended in laminar hot gas flowing in a tube, was modeled and parametrically studied. Due to coupled thermal radiation and thermophoresis, a radially-nonuniform temperature profile develops, leading to sharp, non-uniform radial soot-concentration profiles. The assumption of monodisperse particles leads to over-prediction of thermophoresis. The transport and removal of particles suspended in bubbles rising in a stagnant liquid pool were modeled based on a Eulerian – Monte Carlo method. The bubble hydrodynamics were treated in Eulerian frame, using the Volume-of-Fluid (VOF) technique, while particle equations of motion were numerically solved in Lagrangian frame. The bubbles undergo shape change, and have complex internal circulation, all of which influence the particle removal. Model predictions were also compared with experimental data. Using a resemblance between two-phase flow in microchannels, and in large channels at microgravity, a simple Weber number-based two-phase flow regime map was developed for microchannels. Based on the available air-water experimental data, a criterion for the prediction of conditions that lead to flow regime transition out of the stratified-wavy flow pattern in horizontal annular channels was proposed. The thermocapillary effects on liquid-vapor interface shape during heterogeneous bubble ebullition in microchannels were analytically studied.