With the development of information technique and wireless communication, a vast number of taxis' and ride-sharing cars' trajectory data that provide a rich and detailed source to study on-demand services have been collected. The increasing available trajectory data bring benefits and new challenges to the studies of on-demand services. To provide an overview of the benefits and challenges brought by the trajectory data, we provide a survey on recent studies of trajectory analysis (refer to analyzing trajectory datasets) for on-demand services in this paper. Our purposes are at least trifold. First, we highlight the value of trajectory data in understanding on-demand services and discuss the procedures of retrieving information for the demand part and the supply part from raw trajectory data. Second, we categorize related studies into three parts (the demand part, the supply part, and the mixed part) and review the significant findings. For the demand part, we focus on the models proposed for describing and explaining the spatial-temporal characteristics of observed trips. Methods or models proposed for describing trip statistics, scaling laws of trips, and dynamics of ridership are reviewed. We summarize four types of factors that influence the spatial-temporal patterns of demands. For the supply part, we focus on the models proposed for describing the spatial-temporal characteristics of available taxis/ride-sharing cars and modeling the behavior of drivers (i.e., passenger-search behavior and route choice behavior) to explain the spatial-temporal patterns of taxi/ride-sharing supplies. For the mixed part, we focus on studies that apply the uncovered demands/supplies patterns to design recommendation systems and pricing strategies. Third, we discuss the future directions on collecting/releasing trajectory data and future research directions to advance the understanding of on-demand services.