Beautiful interference phenomena should be seen in many spin-dependent observables for the collision of spin-half hadrons. The phenomena occur both in the collision of charged particles and in the collision of neutral particles with charged particles. Of most direct interest are the reactions pp→pp, np→np, and Λp→Λp. Much information about the phases of the helicity-flip amplitudes near the forward direction can be obtained from the measurement of the interference. Detailed expressions are given for many experimental observables in the interference region,and the extraction of the hadronic amplitudes is discussed in depth. The existence of a new type of "enhanced" order-α correction to the hadronic amplitudes is exhibited and its consequences are explored. In particular the role of electromagnetically induced helicity flip outside the interference regions is stressed and shown to complicate the interpretation of the small measured values of the polarization at Fermilab energies.