Periodic open cellular structures (POCS) represent a promising new class of structured internals as next-generation catalyst supports in reactors or structured packing elements in separation columns. POCS feature a well-defined morphology and can be fabricated with high reproducibility even for complex geometries by means of additive manufacturing. This results in a uniform and easily controllable flow field, which allows for adjusting the heat and mass transport processes to realize optimal process conditions. We review the fundamentals of POCS, including design and manufacturing as well as transport phenomena for single- and multiphase systems. Moreover, we review recent POCS applications in reaction and separation processes and consider promising future application fields. The exceptional transport characteristics of POCS facilitate the design of highly efficient, flexible, resilient, and safe processes, which is key for achieving process intensification toward a sustainable future.