The General Antiparticle Spectrometer (GAPS) will carry out a sensitive dark matter search by measuring low-energy ($mathrm{E} < 0.25 mathrm{GeV/nucleon}$) cosmic ray antinuclei. The primary targets are low-energy antideuterons produced in the annihilation or decay of dark matter. At these energies antideuterons from secondary/tertiary interactions are expected to have very low fluxes, significantly below those predicted by well-motivated, beyond the standard model theories. GAPS will also conduct low-energy antiproton and antihelium searches. Combined, these observations will provide a powerful search for dark matter and provide the best observations to date on primordial black hole evaporation on Galactic length scales. The GAPS instrument detects antinuclei using the novel exotic atom technique. It consists of a central tracker with a surrounding time-of-flight (TOF) system. The tracker is a one cubic meter volume containing 10 cm-diameter lithium-drifted silicon (Si(Li)) detectors. The TOF is a plastic scintillator system that will both trigger the Si(Li) tracker and enable better reconstruction of particle tracks. After coming to rest in the tracker, antinuclei will form an excited exotic atom. This will then de-excite via characteristic X-ray transitions before producing a pion/proton star when the antiparticle annihilates with the nucleus. This unique event topology will give GAPS the nearly background-free detection capability required for a rare-event search. Here we present the scientific motivation for the GAPS experiment, its design and its current status as it prepares for flight in the austral summer of 2021-22.