Big Data is an emerging paradigm and has currently become a strong attractor of global interest, specially within the transportation industry. The combination of disruptive technologies and new concepts such as the Smart City upgrades the transport data life cycle. In this context, Big Data is considered as a new pledge for the transportation industry to effectively manage all data this sector required for providing safer, cleaner and more efficient transport means, as well as for users to personalize their transport experience. However, Big Data comes along with its own set of technological challenges, stemming from the multiple and heterogeneous transportation/mobility application scenarios. In this survey we analyze the latest research efforts revolving on Big Data for the transportation and mobility industry, its applications, baselines scenarios, fields and use case such as routing, planning, infrastructure monitoring, network design, among others. This analysis will be done strictly from the Big Data perspective, focusing on those contributions gravitating on techniques, tools and methods for modeling, processing, analyzing and visualizing transport and mobility Big Data. From the literature review a set of trends and challenges is extracted so as to provide researchers with an insightful outlook on the field of transport and mobility.