The design and construction of genetic systems, in silico, in vitro, or in vivo, often involve the handling of various pieces of DNA that exist in different forms across an assembly process: as a standalone "part" sequence, as an insert into a carrier vector, as a digested fragment, etc. Communication about these different forms of a part and their relationships is often confusing, however, because of a lack of standardized terms. Here, we present a systematic terminology and an associated set of practices for representing genetic parts at various stages of design, synthesis, and assembly. These practices are intended to represent any of the wide array of approaches based on embedding parts in carrier vectors, such as BioBricks or Type IIS methods (e.g., GoldenGate, MoClo, GoldenBraid, and PhytoBricks), and have been successfully used as a basis for cross-institutional coordination and software tooling in the iGEM Engineering Committee.