Large surveys of galaxy clusters with the Hubble and Spitzer Space Telescopes, including CLASH and the Frontier Fields, have demonstrated the power of strong gravitational lensing to efficiently deliver large samples of high-redshift galaxies. We extend this strategy through a wider, shallower survey named RELICS, the Reionization Lensing Cluster Survey. This survey, described here, was designed primarily to deliver the best and brightest high-redshift candidates from the first billion years after the Big Bang. RELICS observed 41 massive galaxy clusters with Hubble and Spitzer at 0.4-1.7µm and 3.0-5.0µm, respectively. We selected 21 clusters based on Planck PSZ2 mass estimates and the other 20 based on observed or inferred lensing strength. Our 188-orbit Hubble Treasury Program obtained the first high-resolution near-infrared images of these clusters to efficiently search for lensed highredshift galaxies. We observed 46 WFC3/IR pointings (∼200 arcmin 2 ) with two orbits divided among four filters (F105W, F125W, F140W, and F160W) and ACS imaging as needed to achieve single-orbit depth in each of three filters (F435W, F606W, and F814W). As previously reported by Salmon et al., we discovered 322 z ∼ 6 − 10 candidates, including the brightest known at z ∼ 6, and the most spatially-resolved distant lensed arc known at z ∼ 10. Spitzer IRAC imaging (945 hours awarded, plus 100 archival) has crucially enabled us to distinguish z ∼ 10 candidates from z ∼ 2 interlopers. For each cluster, two HST observing epochs were staggered by about a month, enabling us to discover 11 supernovae, including 3 lensed supernovae, which we followed up with 20 orbits from our program. We delivered reduced HST images and catalogs of all clusters to the public via MAST and reduced Spitzer images via IRSA. We have also begun delivering lens models of all clusters, to be completed before the JWST GO Cycle 1 call for proposals.