I propose that archaeologists, in pursuing a renewed interest in studying technological change, construct general theories and models of invention processes. As an example, this paper presents the “cascade” model for investigating invention processes in the context of “complex technological systems.” Building on the recognition that the vision of a new complex technological system is often obvious, the cascade model asserts that the hard work of invention takes place in a series of invention “cascades,” as people strive to achieve acceptable values of a new technology's core or critical performance characteristics during life-history processes (i.e., fashioning a prototype, replication or manufacture, use, and maintenance). The cascade model is illustrated by means of the nineteenth-century electromagnetic telegraph, and implications are drawn for studying invention processes in the complex technological systems of small-scale societies.