There is wide interest in the results of studies of the dynamics of satellites of planets. Such data are needed to determine the physical properties of celestial bodies, and they may be able to provide information about the origins and evolution of the solar system. The general approach to studying the dynamics of satellites involves developing models for the motion and ephemerides based on observational data. Ephemerides are required to prepare and launch space missions to other planets and help discover new celestial bodies. High-precision astrometric coordinates of the principal satellites of Jupiter, Saturn, and Uranus are derived from photometric observations of occultations and eclipses of these satellites. To this end, worldwide observing campaigns have been organized. Enhancement in the precision of ephemerides can be obtained not only by increasing the accuracy of observations, but also by expanding the time interval covered by the observations. Many new, distant satellites of the major planets were discovered in the early 21st century. However, observations of these satellites are scarce and were obtained over short time intervals; as a result, some of these satellites were lost. To date, 179 natural satellites are known. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).