Large collecting area x-ray telescopes are designed to study the early Universe, trace the evolution of black holes, stars and galaxies, study the chemical evolution of the Universe, and study matter in extreme environments. The Constellation-X mission (Con-X), planned for launch in 2016, will provide ~ 104 cm2 collecting area with 15 arc-sec resolution, with a goal of 5 arc-sec. Future missions require larger collecting area and finer resolution. Generation-X (Gen-X), a NASA Visions Mission, will achieve 100 m2 effective area at 1 keV and angular resolution of 0.1 arc-sec, half power diameter. We briefly describe the Con-X flowdown of imaging requirements to reflector figure error. To meet requirements beyond Con-X, Gen-X optics will be thinner and more accurately shaped than has ever been accomplished. To meet these challenging goals, we incorporate for the first time active figure control with grazing incidence optics. Piezoelectric material will be deposited in discrete cells directly on the back surface of the optical segments, with the strain directions oriented parallel to the surface. Differential strain between the two layers of the mirror causes localized bending in two directions, enabling local figure control. Adjusting figure on-orbit eases fabrication and metrology. The ability to make changes to mirror figure adds margin by mitigating risk due to launch-induced deformations and/or on-orbit degradation. We flowdown the Gen-X requirements to mirror figure and four telescope designs, and discuss various trades between the designs.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.