This chapter discusses patient appointment scheduling that manages the patient inflow to the healthcare delivery system while satisfying patient needs. It directly affects the operations within the healthcare system and the matrices related to patient outcomes, patient safety, accessibility and timely care. Patient appointment scheduling is complex and challenging due to the uncertainties associated with patient demands, disease progression, treatments, procedures, supporting services and other environmental factors, such as regulations, reimbursement, etc. To manage these uncertainties, simulation or stochastic modeling techniques are frequently used to tackle this class of scheduling problems. This chapter provides an overview of both techniques and demonstrates each technique in an outpatient clinic setting and in a surgery scheduling setting respectively.