We discuss the fundamental role of correlation functions in optical wave fields. These functions determine important properties such as the spectrum, the state of polarization, and the state of coherence of light. These properties generally change on propagation, even when the field travels through free space. Two sources which have the same spectrum and the same state of polarization can produce fields whose spectrum and state of polarization are different. These effects can be understood by considering certain correlation functions and the laws which govern their propagation. © 2008 American Association of Physics Teachers.