The emergence of vehicle automation and its subsequent growth has led to new transport service offerings, generally known as Autonomous Mobility Services (AMS), that have the potential to facilitate or even replace human-operated vehicles. AMS contains different forms of potential mobility options which may contradict current transport modal concepts in terms of functionalities. For example, an autonomous shuttle bus which is a form of autonomous transit may serve similarly as an autonomous taxi/robo-taxi in terms of functionalities, coinciding with the concept of Shared Autonomous Mobility Services (SAMS). Even if the functionalities or operational principles are different, peoples' perceptions of sharing rides in any of these services may be alike. Apart from these confusions in functionalities mentioned above, peoples' attitudes and acceptance of AMS, once it's implemented in any form in the public road environment, remains a significant research aspect. To address these issues, this thesis tried to first clearly distinguish different types of AMS. Second, it tried to assemble the progress till now in acceptance-related research of AMS while reviewing the previous study approaches, outcomes, policy implications, and future research directions. Third, this study attempted to understand the acceptance of AMS using statistical and deep learning approaches leveraging both survey and social media data. Fourth, this study tried to present the consequent applicabilities and limitations of using both types of data sources for autonomous vehicle acceptance research. Eventually, this thesis intends to present an overall idea of the AMS acceptance research with future directions leveraging both data sources in an individualistic or combined manner.