The review surveys eight subdivisions within astrodynamics: geometry, coordinate systems and ephemerides; astrodynamic constants (including heliocentric, genocentric, lunar and planetary, and atmospheric constants); orbit determination; orbit perturbations (gravitational and nongravitational); orbit prediction (using both special and general perturbation techniques); applications (orbit selection and optimization, low thrust orbits, geocentric orbits, lunar, planetary and interplanetary orbits); observation theory; and attitude dynamics. Each subdivision is introduced and a number of the outstanding research papers in each area are mentioned. Specifically, an effort is made to delineate voids in our knowledge and to point up areas of profitable future research in astrodynamics. (Author).