In the modern appointment scheduling literature various approaches have been proposed. Some of them are simulation-based, but these have the obvious shortcoming that the resulting guidelines tend to be case-specific. Other approaches cannot handle relevant characteristics of healthcare processes. The goal of this dissertation is to develop an appointment scheduling methodology that covers realistic healthcare settings, and that outperforms existing methods. The main idea behind our approach is to cast appointment scheduling in a queueing-theoretic framework where an objective function is minimized. To overcome the intrinsic complexity of the problem we study various simplification approaches. In the first place, we approximate the service times by their phase-type counterparts, thus facilitating a fast and efficient recursive procedure for the evaluation of the objective function. We show in detail how various healthcare-specific features, such as walk-ins and no-shows, can be incorporated in this approach. Furthermore, we extend the framework from a single service provider to a two-node tandem system.Besides the phase-type approach, we have developed an alternative approach that uses the actual service-time distribution. In addition, we consider the steady-state version of the appointment scheduling problem, corresponding with the situation in which a large number of patients are scheduled. For this limiting setting we provide insightful analytical results relying on a heavy-traffic approximation. Our general conclusion is that the preferred technique is the phase-type approach, which outperforms competing approaches in the literature almost uniformly. We provide a webtool that implements this approach, which can be used directly by practitioners in healthcare.