Flow expressions describe sequential and concurrent flows of entities, such as control, messages, commands, jobs, and resources, through system software components, such as programs, procedures, modules, and processes. They consist of regular expressions extended with cyclic and interleaving operators and a synchronization facility. The language of flow expressions is defined and some of its formal properties are presented. Applications are exhibited in the modeling of concurrent programs, the description of operating system architectures, the specification and solution of synchronization problems, the flow and description of command languages, and in systems analysis and verification.