Ion velocity space distributions measured with Los Alamos/Garching instruments on ISEE 1 and 2 across the earth's bow shock have revealed that the nearly perpendicular shock reflects some fraction of the incident solar wind ions over a wide range of Mach numbers (MA≂2.0-12.4). The relative density of the reflected ions varies from 1-3% of the solar wind density at MA≈2 to 15-25% at MA=8-12, in qualitative agreement with computer simulations and with predictions that indicate that such ions are needed to provide essential dissipation at the shock. These ions gyrate about B in the plasma rest frame with a speed of ~2 vin, where rin is the normal component of the solar wind flow, and their density increases by ~2 orders of magnitude at the foward end of the ''foot'' of the shock profile ~0.7 ion gyroradii upstream from the shock ramp. This is substantial evidence that the bulk of these ions have been reflected at the shock in a nearly specular fashion. Depending on the shock geometry, some low numbers of reflected-gyrating ions are sometimes observed a few gyroradii ahead of the outer edge of the foot. Model calculations suggest that these additional ions are produced by non-specular reflection of a much smaller fraction of the incident solar wind. Downstream of the shock ramp, the secondary ions gyrate with a slightly higher speed, vg≈2.15 vin, in the downstream rest frame. Individual groups of gyrating ions rapidly disperse in velocity space to form a high-energy torus centered at the bulk velocity of the distributions. Downstream ion toruses are most clearly seen, sometimes persisting for many minutes, when the shock Mach number is low. Downstream of highly supercritical shocks (M≫3). the distributions are more turbulent. In either case, the distribution retains some non-Maxwellian features for a long time downstream from the ramp, in accordance with earlier observations. Reflected-gyrating ions have also been identified in a number of crossings with more oblique field orientations (0nB>45. i.e., for quasi-perpendicular shocks). Specularly reflected ions play an important role in producing downstream ion thermalization for all 0nB>45¿, being relatively more important the higher is the Mach number.