The Sloan Digital Sky Survey V (SDSS-V) is an all-sky spectroscopic survey of >6 million objects, designed to decode the history of the Milky Way, reveal the inner workings of stars, investigate the origin of solar systems, and track the growth of supermassive black holes across the Universe. The Local Volume Mapper (LVM) is a facility designed to provide a contiguous 2,500 deg(2) integral-field survey over a 3.5 year period from Las Campanas Observatory in Chile. In this paper we provide an overview and status update for the LVM instrument (hereafter LVM-I). Each integral-field unit's spaxel probes linear scales that are sub-parsec (Milky Way) to similar to 10 pc (Magellanic Clouds) which is accomplished with an angular diameter of 36.9". LVM's spectral resolution is R = lambda/Delta lambda similar to 4, 000 which probes velocities of 33 kms(-1) (1 sigma) from 365 nm to 950 nm. LVM uses four 16-cm telescopes feeding three spectrographs. One telescope carries the bulk of the science load with similar to 1,800 fibers coupled to the field via a pair of lenslet arrays, two telescopes are used to measure the night sky spectra in fields that flank the science field, and a fourth telescope contemporaneously monitors bright standard stars to determine atmospheric extinction. We expect LVM-I to deliver percent-level precision on important line ratios down to a few Rayleigh. The three spectrographs are being built by Winlight corporation in France based on those for the Dark Energy Spectroscopic Instrument (DESI). In this paper we present the high-level system design of LVM-I including the lenslet-coupled fiber IFUs, telescopes, guiding+acquisition system, calibration systems, enclosures, and spectrographs.