Spin and orbital angular momentum both play essential roles in applications of quantum mechanics to measurement, communication, and information processing. Most introductory quantum mechanics courses cover the spin of electrons in detail, but photons are a little more subtle: spin appears in disguise, showing up as circular polarization, while orbital angular momentum manages to be present even for photons moving in a straight line. In addition, the gauge invariance of electromagnetism means that only two independent spin states appear for the photon (two polarization states), not the three states that would normally be expected for a spin-1 particle like a photon. In this chapter, the angular momenta of electrons and photons are investigated, and the spin- \(1\over 2\) electron spin is used as a model for more general two-state systems.