The ability to controllably rotate, align, or freely spin microparticles in optical tweezers greatly enhances the manipulation possible. A variety of different techniques for achieving alignment or rotation have been suggested and demonstrated. Although these methods are diverse, employing specially shaped particles, birefringent particles, multiple trapping beams, complex beam profiles, vortex modes, plane polarised beams, circularly polarised beams, or other methods, the fundamental principle - that optical torque results from the exchange of electromagnetic angular momentum between the trapping beam and the particle - remains the same. The symmetry of both the particle and the beam play a central role in the transfer of angular momentum. We discuss this in detail, with particular attention paid to the special case of optical torque exerted by an incident beam with zero angular momentum.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.