Modular autonomous vehicles (MAVs) represent a transformative paradigm in the rapidly advancing field of autonomous vehicle technology. The integration of modularity offers numerous advantages, poised to reshape urban mobility systems and foster innovation in this emerging domain. Although publications on MAVs have only gained traction in the past five years, these pioneering efforts are critical for envisioning the future of modular mobility. This work provides a comprehensive review of industry and academic contributions to MAV development up to 2024, encompassing conceptualization, design, and applications in both passenger and logistics transport. The review systematically defines MAVs and outlines their technical framework, highlighting groundbreaking efforts in vehicular conceptualization, system design, and business models by the automotive industry and emerging mobility service providers. It also synthesizes academic research on key topics, including passenger and logistics transport, and their integration within future mobility ecosystems. The review concludes by identifying challenges, summarizing the current state of the art, and proposing future research directions to advance the development of modular autonomous mobility systems.