Self-driving labs (SDLs) combine fully automated experiments with artificial intelligence (AI) that decides the next set of experiments. Taken to their ultimate expression, SDLs could usher a new paradigm of scientific research, where the world is probed, interpreted, and explained by machines for human benefit. While there are functioning SDLs in the fields of chemistry and materials science, we contend that synthetic biology provides a unique opportunity since the genome provides a single target for affecting the incredibly wide repertoire of biological cell behavior. However, the level of investment required for the creation of biological SDLs is only warranted if directed toward solving difficult and enabling biological questions. Here, we discuss challenges and opportunities in creating SDLs for synthetic biology.