Next Generation Space Telescope (NGST) is under design study for proposed launch around 2008. It will take over the task of Hubble Space Telescope (HST) and provide much more detailed information about celestial objects. Present large telescopes both in space and on the ground contain aspheric mirrors, called Ritchey-Chretien type. As the size of the telescope becomes larger and the optical quality is requested to be higher, reaching the diffraction limit, more accurate optical testing methods are required. However, there are few testing methods which can achieve the required accuracy for aspheric optics, and none of them has achieved it with certainty. The failure of producing the primary mirror of the Hubble Space Telescope to meet specification is a good example. Moreover, testing aspheric mirrors of large convex form adds the difficulty to extreme. In this paper, space telescopes and large ground-based telescopes are surveyed and testing methods for aspheric optics are reviewed. a method of testing aspheric convex mirrors is suggested.