We survey theoretical and experimental/observational results on general-relativistic spin (rotation) effects in binary systems. A detailed discussion is given of the two-body Kepler problem and its first post-Newtonian generalization, including spin effects. Spin effects result from gravitational spin-orbit and spin-spin interactions (analogous to the corresponding case in quantum electrodynamics) and these effects are shown to manifest themselves in two ways: a) precession of the spinning bodies per se and b) precession of the orbit (which is further broken down into precessions of the argument of the periastron, the longitude of the ascending node and the inclination of the orbit). We also note that ambiguity that arises from use of the terminology frame-dragging, de Sitter precession and Lense-Thirring precession, in contrast to the unambiguous reference to spin-orbit and spin-spin precessions. Turning to one-body experiments, we discuss the recent results of the GP-B experiment, the Ciufolini-Pavlis Lageos experiment and lunar-laser ranging measurements (which actually involves three bodies). Two-body systems inevitably involve astronomical observations and we survey results obtained from the first binary pulsar system, a more recently discovered binary system and, finally, the highly significant discovery of a double-pulsar binary system.