We are developing a novel concept for mobility, and studying fundamental research issues on dynamics and control of the mobile robot. The robot, called Gyrover, is a single-wheel vehicle with an internal gyroscope that provides mechanical stabilization and steering capability. This configuration conveys significant advantages over multi-wheel, statically stable vehicles, including good dynamic stability and insensitivity to attitude disturbances; high manoeuvrability; low rolling resistance; ability to recover from falls; and amphibious capability. In this paper we present the design, analysis and implementation of the robot, as well as the associated research issues and potential applications.