The food systems of the National Aeronautics and Space Administration (NASA) have evolved tremendously since the early manned spaceflights of the 1960s. To date, NASA's mission focus has been limited to exploration of low Earth orbit (LEO), and the agency's prepackaged food systems have been adequate to enable success of their parent programs. With NASA's mission focus increasing to achieve manned space exploration of the Martian surface, the agency is considering a significant departure from the prepackaged food systems of current and past space programs. NASA's Advanced Food Technology (AFT) project is presently investigating the introduction of a bioregenerative food system to support long duration habitat missions to the Martian surface. A bioregenerative food system is expected to impart less of a burden on critical mission resources, such as mass and volume, than a prepackaged, shelf-stable system. This review provides an introduction to past and present spaceflight food systems, and provides a broad examination of the research conducted to date to enable crop production and food processing on the Martian surface.