One of the most fundamental issues in evolutionary biology is the transition from unicellularity to multicellularity, and the cellular differentiation that accompanies it. In this talk I will describe recent results on two types of "multicellular" systems, that produced by many unicellular organisms acting collectively, and that of permanently multicellular organisms. In both, the biology of chemotaxis, metabolism and cell-cell signaling is intimately connected to the physics of buoyancy, diffusion, and mixing. These results include the discovery in bacterial suspensions of large scale coherence characterized by transient, recurring vortex streets and high-speed jets of cooperative swimming. Complementary experiments on photosynthetic colonial green algae reveal that the flagella on the thousands of surface cells, which confer phototactic motility, also play a crucial role in driving advective transport, thus allowing larger organisms to circumvent a diffusive bottleneck to nutrient uptake. In both cases, these large Peclet number flows fundamentally alter the transport of metabolites and chemical messengers in such systems. Implications for evolutionary transitions are discussed.