STAR-X is a MIDEX mission proposed to NASA in December 2021 and selected in 2022 for further study. Comprising an X-ray telescope (XRT) provided by GSFC and MIT, a UV telescope (UVT) provided by the University of Colorado, and a spacecraft (SC) provided by Ball Aerospace, STAR-X is designed to conduct time-domain survey and to respond rapidly to transient events discovered by other observatories such as LIGO, Rubin LSST, Roman WFIRST, and SKA. The key features of the XRT are its excellent PSF (2.5 arc-seconds half-power diameter), large effective area (1,800 cm2 at 1 keV), and large field of view (1 deg2), making it more than an order of magnitude more capable and more sensitive than Chandra and Swift/XRT to conduct survey and to find and study transient sources. The UVT has a 30-cm aperture with 5 filters covering the 160nm to 340nm band, providing simultaneous spectral coverage with the XRT and enabling reverberation mapping of accretion disk geometries around black holes. The SC is highly autonomous and is capable of fast slewing, enabling efficient raster scans and time-domain surveys. In particular, in combination with a state-of-the-art mission operations center at the University of Colorado, the SC can respond to targets of opportunity within 2 hours 90% of the time. With its nearly equatorial low-earth orbit, STAR-X’s telescopes will have low particle background, enabling them to have unprecedented sensitivity for measuring faint diffuse emissions from clusters of galaxies. STAR-X is a timely response to Astro2020’s recommendation for a space-based, sustaining time-domain and multi-messenger program. Data will be archived in the HEASARC.