Detailed, high-resolution numerical simulations have been performed of the buoyancy-driven motion of deformable, chemically reacting bubble and droplet swarms. Mass transfer rates and chemical reaction selectivities were determined and a comparison is presented between the results for bubble/droplet swarms and single bubbles. The mixing in the wake of bubbles was characterized as well. It was shown that for mixing-sensitive reaction networks, the hydrodynamics of the bubble swarm may significantly impact the reaction selectivity. Four special cases are highlighted, i.e., highly exothermic reactions, heterogeneously catalyzed reactions, animal cell cultures and experiments. The most important outcome of this work is that bubble swarms and the impact of the swarm hydrodynamics on reacting systems can be studied in detail. This is the first study of this kind reported in the literature. Its importance is paramount as knowledge of the unique flow dynamics inside bubble swarms is crucial to understanding the mechanisms controlling mass transport and chemical reactions and is a prerequisite for effective process intensification.