This thesis studies on-demand service platforms (e.g., Deliveroo, Uber), which operate in various sectors such as meal delivery and ride-hailing. By providing timely services, these platforms play an important role in urban logistics. However, they also present challenges, as they operate in dynamic and uncertain environments. This thesis is composed of three main chapters that aim to investigate distinct operational challenges emerging on on-demand service platforms. The first chapter considers the organization of a priority service within a platform that differentiates customers according to their willingness to wait and to pay. The second chapter studies the problem of a platform that balances supply and demand across its service area through dynamic pricing, customer admission, and driver repositioning. Finally, the last chapter examines the integration of public transit transfers into a ride-hailing platform that offers first-mile and last-mile services to its customers, in addition to conventional door-to-door services. Throughout these three chapters, this thesis develops new stochastic optimization models and methodologies, providing managerial insights into the operations of on-demand service platforms.