This paper provides a comprehensive survey of research on appointment scheduling in outpatient services. Effective scheduling systems have the goal of matching demand with capacity so that resources are better utilized and patient waiting times are minimized. Our goal is to present general problem formulation and modeling considerations, and to provide taxonomy of methodologies used in previous literature. Current literature fails to develop generally applicable guidelines to design appointment systems, as most studies have suggested highly situation-specific solutions. We identify future research directions that provide opportunities to expand existing knowledge and close the gap between theory and practice.