Rhenium is an important alloying agent in catalytic materials and superalloys, but the experimental and computational data on its binary alloys are sparse. Only 6 out of 28 Re transition-metal systems are reported as compound-forming. Fifteen are reported as phase-separating, and seven have high-temperature disordered a or chi phases. Comprehensive high-throughput first-principles calculations predict stable ordered structures in 20 of those 28 systems. In the known compound-forming systems, they reproduce all the known compounds and predict a few unreported ones. These results indicate the need for an extensive revision of our current understanding of Re alloys through a combination of theoretical predictions and experimental validations. The following systems are investigated: AgRe star, AuRe star, CdRe star, CoRe, CrRe star, CuRe star, FeRe, HfRe, HgRe star, IrRe, MnRe, MoRe, NbRe, NiRe, OsRe, PdRe, PtRe, ReRh, ReRu, ReSc, ReTa, ReTc, ReTi, ReV, ReW star, ReY, ReZn star, and ReZr ((star) = systems in which the ab initio method predicts that no compounds are stable).