Medieval Islamic mathematicians and astronomers developed a variety of mathematical definitions and computations of the three astrological concepts of houses, rays (or aspects) and progressions. The medieval systems for the astrological houses have been classified by J.D. North and E.S. Kennedy, and the purpose of our paper is to attempt a similar classification for rays and progressions, on the basis of medieval Islamic astronomical handbooks and instruments. It turns out that there were at least six different systems for progressions, and no less than nine different systems for rays. We will investigate the historical relationships between these systems and we will also discuss the authors to whom the systems are attributed in the medieval Islamic sources.