/ AbstractThe DECam Local Volume Exploration survey (DELVE) is a 126-night survey program on the 4-m Blanco Telescope at the Cerro Tololo Inter-American Observatory in Chile. DELVE seeks to understand the characteristics of faint satellite galaxies and other resolved stellar substructures over a range of environments in the Local Volume. DELVE will combine new DECam observations with archival DECam data to cover ~15000 deg$^2$ of high-Galactic-latitude (|b| > 10 deg) southern sky to a 5$σ$ depth of g,r,i,z ~ 23.5 mag. In addition, DELVE will cover a region of ~2200 deg$^2$ around the Magellanic Clouds to a depth of g,r,i ~ 24.5 mag and an area of ~135 deg$^2$ around four Magellanic analogs to a depth of g,i ~ 25.5 mag. Here, we present an overview of the DELVE program and progress to date. We also summarize the first DELVE public data release (DELVE DR1), which provides point-source and automatic aperture photometry for ~520 million astronomical sources covering ~5000 deg$^2$ of the southern sky to a 5$σ$ point-source depth of g=24.3, r=23.9, i=23.3, and z=22.8 mag. DELVE DR1 is publicly available via the NOIRLab Astro Data Lab science platform.