Artificial disc replacements (ADRs) and total disc replacements (TDRs) are based upon two, directly articulating components, resulting in a restricted-motion system that better approximates more normal spinal flexion, extension, and lateral bending. One component may have a concave articulating surface, and the other a convex articulating surface. The radius of curvature of the articulating surface may be smaller in the anterior-to-posterior direction of the ADR than the radius of curvature of the articulating surface in the left-to-right direction of the ADR. Both components are preferably made of a hard material and are highly polished to reduce friction.