This paper looks at the stimulus given by the practice and theory of navigation to certain problems in mathematical astronomy. The need for more accurate techniques of finding latitude and longitude, brought about largely by the great voyages of discovery and exploration as well as an increase in sea trade, gave rise to navigational instrument makers who produced devices of increasing accuracy. These craftsmen also made better measuring devices for the new observatories. Improvements in measurements led not only to new discoveries, but also made greater demands of theories underlying the practice of navigation. This gave impetus to the search for solutions to related problems in mathematical astronomy. Methods and special functions developed in this context were eventually to find application in a much wider range of problems in theoretical physics and engineering.