Astronomers are fairly confident that most stars have planetary systems. After all, why should our Sun be special? But, because of the distances involved, detecting planets around other stars is hard. In this talk, I will survey the various methods of planet detection. Indirect detection of large (Jupiter-sized) planets has become somewhat routine but so far no one has directly imaged small (Earth-like) planets. In this talk I will explain why the problem is hard and try to give a sense of the serious computations that are required to simulate the optical systems that might one day make these planet detections.