The Brookhaven National Laboratory Tandem-AGS accelerator facility has been used since 1986 to generate beams of 16O and 28Si at momenta of 14.6 A·GeV/c and recently 197Au at momenta of up to 11.6 A·GeV/c. In collisions with nuclear targets, these relativistic heavy ion beams are believed to produce nuclear matter at close to the highest baryon densities achievable in the laboratory. The status of the experimental program and theoretical understanding of these interactions will be summarized. Although no unambiguous evidence for new physics (such as the formation of a quark gluon plasma) has been found, a number of interesting features have arisen. In particular, it is clear that the dynamic evolution of these systems is dominated by the creation, interactions, and decays of high-mass excited baryons.