Both Jet-engine propelled aircraft and long-range rockets were first successfully flown during World War II. This led 10 rapid post-war improvements in both, and within two decades we had supersonic airplanes, communication satellites, and trips to the moon. Unmanned probes to Mars and the outer planets followed, as well as the International Space Station. The technology behind these advances is described, along with short biographies of key pioneers. Problems at high Mach numbers are reviewed. Possible future developments are discussed. Mora technical details, including mathematics, are in an appendix.