Adaptive optics for the 30-100 meter class telescopes now being considered will require an extension in almost every area of AO system component technology. In this paper, we present scaling laws and strawman error budgets for AO systems on extremely large telescopes (ELTs) and discuss the implications for component technology and computational architecture. In the component technology area, we discuss the advanced efforts being pursued at the NSF Center for Adaptive Optics (CfAO) in the development of large number of degrees of freedom deformable mirrors, wavefront sensors, and guidestar lasers. It is important to note that the scaling of present wavefront reconstructor algorithms will become computationally intractable for ELTs and will require the development of new algorithms and advanced numerical mathematics techniques. We present the computational issues and discuss the characteristics of new algorithmic approaches that show promise in scaling to ELT AO systems.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.