Emerging transportation technologies (e.g., electric vehicles) and services (e.g., shared mobility) provide efficient, sustainable and cost-effective alternatives to traditional travel modes. However, whether these innovative technologies bring benefits to different population groups in an equal and reasonable manner is still an open question. The various methods applied to evaluate the equity performance of these systems are also not clearly comparable. In this paper, we comprehensively review methods from the existing literature for assessing the equity of a few important system outcomes: accessibility, traffic emissions, and safety. We also identify the existing challenges of analyzing equity for emerging transportation technologies. We unify the existing methodologies into a three-step framework that includes population measurement, cost/benefit measurement and equity assessment, and we summarize the applicable measurements for each step, in detail. A handful of literature focusing on emerging transportation technologies, such as shared mobility and autonomous vehicles, were also identified and surveyed; the methodologies used were found to fit with the three-step framework. We summarize the major findings and discuss promising directions for developing more sophisticated equity assessment methodologies for emerging transportation technologies. Overall, based on a comprehensive review, this paper contributes a framework for assessing the equity of transportation systems that integrates accessibility, traffic emissions, and safety outcomes. The summarized framework can be an overview resource to assist researchers and transportation planners who require equity analysis methods. The research gaps identified also provide directions for equity research on emerging transportation technologies.