Book excerpt: Electric vehicle (EV) sharing services have received growing attention from investors and city dwellers in the decade. However, due to high operating costs and the increasing competition, profitability has become the bottleneck for many EV sharing service providers to succeed in the long run. My dissertation research focuses on developing mathematical models to design finer operational strategies for large-scale EV sharing fleets, especially in the stochastic and unbalanced transportation background. The basic blueprint is to upgrade EV fleet management from myopic strategies to location-based, energy-based, and environment-responsive policies. Specifically, we develop models to incorporate dynamic origin-destination pricing, congestion-responsive deployment, and battery health management into centralized EV sharing systems. First, we consider the dynamic pricing and dispatching of EVs given stochastic, time-varying, and heterogeneous customer demand. The EV operator monitors the fleet distribution and the demand signals to make real-time decisions. We adopt approximate dynamic programming (ADP) methods to solve the system. In particular, we develop neural network value function approximation (VFA) techniques that improve the policy performance. Our case study suggests that, with the demand-responsive pricing instrument, the EV fleet can effectively increase its expected profit, reduce the need for manual rebalancing, and smoothen the electricity usage across time. Next, we further investigate the interaction between the EV fleet and the congested transportation network. We extend the preliminary work to build a spatiotemporal network where the fleet operation and traffic states are captured by an approximated fluid model. The ADP algorithm maintains its effectiveness. We further design VFA methods to meet the learning need in the augmented state space. Numerical results demonstrate the benefit of dispatching vehicles using congestion-aware strategies. Finally, we consider the battery health management problem in an EV sharing fleet. We propose a continuous model to address the joint vehicle charging and moving problems for a large-scale EV sharing system. Under reasonable assumptions, the formulation is reduced to the continuous Kantorovich-Rubinstein transshipment and a battery-related optimization. On this basis, we obtain a near-optimal battery charging/replacing policy. Our model supports a shared EV fleet's decisions on charging device installation, vehicle relocation, and battery charging/replacing.