During 2003--2015, the CERN Axion Solar Telescope (CAST) has searched for $atogamma$ conversion in the 9 T magnetic field of a refurbished LHC test magnet that can be directed toward the Sun. In its final phase of solar axion searches (2013--2015), CAST has returned to evacuated magnet pipes, which is optimal for small axion masses. The absence of a significant signal above background provides a world leading limit of $g_{agamma} < 0.66 times 10^{-10} {rm GeV}^{-1}$ (95% C.L.) on the axion-photon coupling strength for $m_a lesssim 0.02$ eV. Compared with the first vacuum phase (2003--2004), the sensitivity was vastly increased with low-background x-ray detectors and a new x-ray telescope. These innovations also serve as pathfinders for a possible next-generation axion helioscope.