This dissertation presents work on the stochastic modeling and control of service systems, within the broader fields of management science and operations management. The first two chapters focus on the ridesharing industry, while the third chapter studies an online content moderation system. In the first chapter, we develop a closed queueing network model of a ride-hailing system, where cars are conceptualized as jobs circulating through various nodes representing different city regions. By incorporating travel times between these nodes, our model achieves a high degree of generality. We rigorously prove a novel heavy traffic limit theorem for this queueing network, providing an approximation for the original ride-hailing system as the system approaches heavy traffic. In the second chapter, we study a stochastic control problem based on the model presented in the first chapter, but featuring only a singular travel time node. To be more specific, we study a queueing network model motivated by ride-hailing applications where a system manager makes dynamic pricing and dispatch control decisions to maximize the long-run average profit. Since this problem appears analytically intractable, we consider an approximating Brownian control problem in the heavy traffic regime. Under the assumptions of complete resource pooling and common travel time and routing distributions, we exploit an equivalence between the Brownian control problem and a one-dimensional workload formulation. We then solve the workload formulation in closed form by analyzing the corresponding Bellman equation. Using this solution, we propose a policy for the original queueing system and illustrate its effectiveness in a simulation study. In the third chapter, we study the moderation of user-generated content by online platforms, with a particular focus on social media companies. The increased popularity of social media in recent years has led to an explosion of user-generated content. Although a substantial portion of this content is harmless, social media companies bear the crucial responsibility of protecting their users from harmful material. We propose a stochastic modeling framework for an online content moderation system that integrates a machine learning classifier with human moderators. Our focus is on determining which content should be reviewed by human moderators. On the one hand, manual review by human moderators improves the classification accuracy of individual content and improves the accuracy of the machine learning classifier through supervised learning. On the other hand, sending content for human review results in operational congestion-based costs. Through a simulation study, we aim to explore the trade-off between learning and system congestion that arises when the platform sends multiple copies of a piece of content for human review. Finally, we present a related stochastic model for online content moderation via a Bayesian learning framework.