In response to recommendations of the Astronomy Survey Committee of the National Academy of Sciences, NASA formed a science definition team in 1982 to establish science goals for an extreme ultraviolet (EUV) mission in the explorer class. Originally, it was intended that the primary goal of the FUSE mission would be to obtain high and moderate resolution spectroscopic data from approximately 912-1250A. However, a significant conclusion reached by the team was that it is possible to design and build instrumentation to cover the spectral region from approximately 100-1250Å, especially if a glancing incidence telescope optimized for the EUV is used. In this paper, we discuss the optical design and technology trades to be considered in the selection of a telescope for FUSE. A discussion of the advantages and disadvantages of both normal incidence and glancing incidence optical designs is given in terms of maximum glancing angle, collecting area, and physical length. Throughput limitations for normal incidence systems are explored in view of new optical coating technology, i.e., SiC coatings and layered synthetic microstructures (LSMs). Factors contributing to degradation of image quality in terms of rms blur circle radius and field curvature are discussed, and in particular a comparison between Wolter and Wolter-Schwarzschild Type II designs is presented. A number of selected telescopes satisfying the design constraints are compared. Although surface height differences between a Wolter and a Wolter-Schwarzschild may be small, either could be fabricated with the aid of computer controlled polishing presently being developed for cylindrical components.