Understanding the aerodynamic interactions between turbines in a wind farm is essential for maximizing power generation. In contrast to horizontal-axis wind turbines (HAWTs), for which wake interactions between turbines in arrays must be minimized to prevent performance losses, vertical-axis wind turbines (VAWTs) in arrays have demonstrated beneficial interactions that can result in net power output greater than that of turbines in isolation. These synergistic interactions have been observed in previous numerical simulations, laboratory experiments, and field work. This dissertation builds on previous work by identifying the aerodynamic mechanisms that result in beneficial turbine-turbine interactions and providing insights into potential wind farm optimization. The experimental data presented indicates increased power production of downstream VAWTs when positioned offset from the wake of upstream turbines. Comparison with three-dimensional, three-component flow measurements demonstrates that this enhancement is due to flow acceleration adjacent to the upstream turbine, which increase the incident freestream velocity on appropriately positioned downstream turbines. A low-order model combining potential flow and actuator disk theory accurately captures this effect. Laboratory and field experiments were used to validate the model's predictive capabilities, and an evolutionary algorithm was deployed to investigate array optimization. Furthermore, changes in upstream turbine performance are related to variations in the surrounding flow field due to the presence of the downstream rotor. Finally, three-dimensional vortex interactions behind pairs of VAWTs are observed to replenish momentum in the array's wake. These effects are described along with their implications for wind farm design.