Using touch screens presents a number of usability and accessibility challenges for blind people. Most touch screen-based user interfaces are optimized for visual interaction, and are therefore difficult or impossible to use without vision. This dissertation presents an approach to redesigning gesture-based user interfaces to enable blind people to use touch screens. I conducted two formative research studies to motivate and guide the design of accessible touch screens: a combined interview and diary study exploring accessibility challenges experienced by blind people when using technology in mobile contexts, including touch screens; and a lab study exploring differences in how blind and sighted people choose and perform gestures. In addition, I developed three prototypes that introduced new accessible gesture-based interaction techniques: Slide Rule, a set of accessible multi-touch interaction techniques for smartphones; Access Overlays, enhanced touch screen access techniques for large touch screens; and Access Lens, a combined software and hardware prototype that leverages computer vision to enable blind users to perform accessible gestures on uninstrumented surfaces and public touch screen kiosks. This work presents a comprehensive approach to designing new accessible touch screen interaction techniques that support blind users' needs and abilities. The thesis of the dissertation is: "Accessible gesture-based interfaces, designed to support the spatial and tactile abilities of blind people, can enable blind people to effectively use touch screens, including on mobile devices, tablet and tabletop computers, and public information kiosks." [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]