The natural world provides many examples of multiphase transport and reaction processes that have been optimized by evolution. These phenomena take place at multiple length and time scales and typically include gas-liquid-solid interfaces and capillary phenomena in porous media1,2. Many biological and living systems have evolved to optimize fluidic transport. However, living things are exceptionally complex and very difficult to replicate3-5, and human-made microfluidic devices (which are typically planar and enclosed) are highly limited for multiphase process engineering6-8. Here we introduce the concept of cellular fluidics: a platform of unit-cell-based, three-dimensional structures-enabled by emerging 3D printing methods9,10-for the deterministic control of multiphase flow, transport and reaction processes. We show that flow in these structures can be 'programmed' through architected design of cell type, size and relative density. We demonstrate gas-liquid transport processes such as transpiration and absorption, using evaporative cooling and CO2 capture as examples. We design and demonstrate preferential liquid and gas transport pathways in three-dimensional cellular fluidic devices with capillary-driven and actively pumped liquid flow, and present examples of selective metallization of pre-programmed patterns. Our results show that the design and fabrication of architected cellular materials, coupled with analytical and numerical predictions of steady-state and dynamic behaviour of multiphase interfaces, provide deterministic control of fluidic transport in three dimensions. Cellular fluidics may transform the design space for spatial and temporal control of multiphase transport and reaction processes.