Cells are able to navigate environments, communicate, and build complex patterns by initiating gene expression in response to specific signals. Engineers need to harness this capability to program cells to perform tasks or build chemicals and materials that match the complexity seen in nature. This review describes new tools that aid the construction of genetic circuits. We show how circuit dynamics can be influenced by the choice of regulators and changed with expression “tuning knobs.” We collate the failure modes encountered when assembling circuits, quantify their impact on performance, and review mitigation efforts. Finally, we discuss the constraints that arise from operating within a living cell. Collectively, better tools, well-characterized parts, and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the atomic manufacturing of functional materials.