The tokamak reactor becomes a more attractive fusion power source if it can operate in steady state, and at high fusion power density, with low recirculating power. This implies that a ‘‘steady-state advanced tokamak’’ must achieve both high beta and high confinement, consistent with a high fraction of the total plasma current being carried by the bootstrap effect. The most attractive mode of operation to fulfill these requirements involves a reversal of the global magnetic shear, dq/dr, in the plasma core. This allows self-consistency between the radial profile of the bootstrap current and that of the total current, while simultaneously reducing turbulent transport in the plasma core and increasing magnetohydrodynamic (MHD) stability. In this paper both theoretical and experimental work on the steady-state advanced tokamak are reviewed, and we point to new research areas that need to be pursued to make this concept a reality. Presently operating devices can make strong contributions in this research area, and future devices should be designed with the capability to access, investigate, and exploit this operating mode.