We present the Sloan Digital Sky Survey V Local Volume Mapper (LVM). The LVM is an integral-field spectroscopic survey of the Milky Way, Magellanic Clouds, and a sample of local volume galaxies, connecting resolved parsec-scale individual sources of feedback to kiloparsec-scale ionized interstellar medium (ISM) properties. The 4 yr survey covers the southern Milky Way disk at spatial resolutions of 0.05–1 pc, the Magellanic Clouds at 10 pc resolution, and nearby large galaxies at larger scales totaling >4300 deg2 of sky and more than 55M spectra. It utilizes a new facility of alt–alt mounted siderostats feeding 16 cm refractive telescopes, lenslet-coupled fiber optics, and spectrographs covering 3600–9800 Å at R ∼ 4000. The ultra-wide-field integral-field unit has a diameter of 0.°5 with 1801 hexagonally packed fibers of 35.″3 apertures. The siderostats allow for a completely stationary fiber system, avoiding instability of the line-spread function seen in traditional fiber feeds. Scientifically, LVM resolves the regions where energy, momentum, and chemical elements are injected into the ISM at the scale of gas clouds, while simultaneously charting where energy is being dissipated (via cooling, shocks, turbulence, bulk flows, etc.) to global scales. This combined local and global view enables us to constrain physical processes regulating how stellar feedback operates and couples to galactic kinematics and disk-scale structures, such as the bar and spiral arms, as well as gas in- and outflows.