The tremendous growth of positioning technologies and GPS enabled devices has produced huge volumes of tracking data during the recent years. This source of information constitutes a rich input for data analytics processes, either offline (e.g. cluster analysis, hot motion discovery) or online (e.g. short-term forecasting of forthcoming positions). This paper focuses on predictive analytics for moving objects (could be pedestrians, cars, vessels, planes, animals, etc.) and surveys the state-of-the-art in the context of future location and trajectory prediction. We provide an extensive review of over 50 works, also proposing a novel taxonomy of predictive algorithms over moving objects. We also list the properties of several real datasets used in the past for validation purposes of those works and, motivated by this, we discuss challenges that arise in the transition from conventional to Big Data applications. CCS Concepts: Information systems > Spatial-temporal systems; Information systems > Data analytics; Information systems > Data mining; Computing methodologies > Machine learning Additional Key Words and Phrases: mobility data, moving object trajectories, trajectory prediction, future location prediction.