The history of complexity

Summary form only given. We describe several trends in the history of computational complexity, including: the early history of complexity; the development of NP-completeness and the structure of complexity classes; how randomness, parallelism and quantum mechanics has forced us to reexamine our notions of efficient computation and how computational complexity has responded to these new models; the meteoric rise and fall of circuit complexity; and the marriage of complexity and cryptography and how research on a cryptographic model led to limitations of approximation.