The increasing population across the globe makes it essential to link smart and sustainable city planning with the logistics of transporting people and goods, which will significantly contribute to how societies will face mobility in the coming years. The concept of smart mobility emerged with the popularity of smart cities and is aligned with the sustainable development goals defined by the United Nations. A reduction in traffic congestion and new route optimizations with reduced ecological footprint are some of the essential factors of smart mobility; however, other aspects must also be taken into account, such as the promotion of active mobility and inclusive mobility, encouraging the use of other types of environmentally friendly fuels and engagement with citizens. The Internet of Things (IoT), Artificial Intelligence (AI), Blockchain and Big Data technology will serve as the main entry points and fundamental pillars to promote the rise of new innovative solutions that will change the current paradigm for cities and their citizens. Mobility-as-a-service, traffic flow optimization, the optimization of logistics and autonomous vehicles are some of the services and applications that will encompass several changes in the coming years with the transition of existing cities into smart cities. This paper provides an extensive review of the current trends and solutions presented in the scope of smart mobility and enabling technologies that support it. An overview of how smart mobility fits into smart cities is provided by characterizing its main attributes and the key benefits of using smart mobility in a smart city ecosystem. Further, this paper highlights other various opportunities and challenges related to smart mobility. Lastly, the major services and applications that are expected to arise in the coming years within smart mobility are explored with the prospective future trends and scope.