Overview: The Ultraviolet Explorer (UVEX) is one of two missions selected by NASA to conduct mission concept studies as a Medium Explorer (MIDEX). NASA plans to select one Medium Explorer mission in 2024 to proceed with implementation. Launching no earlier than 2027, UVEX would undertake a synoptic survey of the entire sky in the near-UV and far-UV, probing the dynamic universe with a sensitivity more than 50 times better than GALEX. UVEX would also have a powerful broadband spectroscopic capability. UVEX would address fundamental questions from the Astro2020 Decadal Survey, and study the evolution of low-metallicity, low-mass galaxies. UVEX time-domain surveys could probe the aftermaths of gravitational wave-discovered compact object mergers, discover fast UV transients, and diagnose the early stages of explosive phenomena.