This paper surveys the results established so far by the on-going research on the planetary theories in Arabic astronomy. The most important results of the Maragha astronomers are gathered here for the first time, and new areas for future research are delineated. The conclusions reached demonstrate that the Arabic astronomical works mentioned here not only elaborate the connection between Arabic astronomy and Copernicus, but also that such activities, namely the continuous reformulation of Greek astronomy, were not limited to a specific group of astronomers or to a specific geographical area. It is shown that such activities were spread over a period of more than seven hundred years, from the early eleventh till the sixteenth century, and over an area stretching from the Andalusian peninsula in the west to the farthest reaches of Central Asia in the east.