Recent advances in computing and artificial intelligence have enabled the development of various emerging vehicle technologies, e.g., autonomous vehicles (AV) and modular autonomous vehicles (MAV). These technologies bring new scientific and engineering problems challenging transportation researchers and practitioners. This dissertation aims to develop a suite of scalable computational and analytical tools for designing and analyzing next-generation transportation systems with the MAV technologies. Also, we intend to empirically study the system impacts in terms of the quality of service, energy implications, and inequality impacts. For MAV system design, we develop a methodological framework centering at theoretical properties of the optimal system design under two system settings: i) shuttle systems consisting of one origin and one destination, ii) corridor systems where vehicles travel along a set of stations. We mathematically prove a series of elegant properties of system design variables when the system optimum is reached. These properties are then used to decompose the spatiotemporal correlation between the system design variables, which allows us to formulate the system design into separable continuum approximation models. Also, these properties are used to derive valid inequalities that can dramatically reduce the solution space of the system design problem. As a result, they can be applied to solve discrete formulations of the problem to expedite the search for the exact optimal design. Extensive numerical studies are conducted to evaluate the computation performance of the proposed solution methods. Results indicate that discrete models expedited by the theoretical properties find optimal system design more quickly. The continuous models, instead, offer highly accurate near-optimal design in less than one second. These two methods complement each other in terms of the solution accuracy and computation time. With the methodological framework, we also conduct extensive experiments to assess the impacts of the MAV technologies on system performance. We compare the energy cost for vehicle operations, the passenger waiting cost, and the total system cost between the proposed MAV transportation system and a benchmark system where fixed capacity vehicles are operated. Results reveal that by dynamically adjusting the vehicle capacity to accommodate the passenger demand, MAVs consistently decrease the energy cost of shuttle systems and corridor systems in a range of parameter settings. Meanwhile, the passenger waiting cost are reduced or remain at least the same as the fixed capacity operation in most cases. In a few cases the passenger waiting cost is slightly increased. However, the slight increase in the passenger waiting cost is compensated by the large reduction in the energy cost, resulting in a decrease in the total system cost. Thus, MAVs increase the energy efficiency and quality of services in the majority of system settings. Finally, as the first step to investigate the potential equity impacts of the MAV technologies, we develop an analysis framework for quantifying the inequality impacts of AVs. The framework is built on a state-of-the-art multi-agent transportation simulator, MATSim, by incorporating the influence of individual demographics on travel decisions and private AVs. The simulation model generates individual-level daily travel itineraries that can be used to analyze benefits / costs of AVs. We apply the framework to analyze the inequality impacts of AV systems in the Tampa Bay Region in the 2040 planning scenario. Results reveal the capability of the proposed methodological framework in analyzing the inequality impacts of AV systems. Further, an AV system with private AVs and low market penetration rates may not improve the performance of a transportation system as expected due to the additional empty vehicle trips induced by AV operations. However, it leads to a more even outcome distribution between homogeneous individuals and among the geographic space in the Tampa Bay Region. It may not change the disparity direction of the transportation outcome distributions between different population subgroups but will affect the magnitude of the disparity. Whether the disparity between groups will be widened or bridged depends on the specific outcomes and the groups being analyzed. Overall, this dissertation offers scalable numerical and analytical tools for designing and analyzing MAV transportation systems. These models and algorithms can be used as benchmarks for researchers to evaluate the performance of their methods in future studies. They can also be used by transportation practitioners to design and analyze MAV transportation systems when the technology is mature. Further, findings from the extensive empirical case studies add to the body of knowledge of system properties of MAV transportation systems and their impacts to society including the level of service, energy implications, and inequality impacts. These results will offer managerial insights for future transportation planners and operators.