How to utilize multi-source and heterogeneous spatio-temporal data to achieve accurate trajectory prediction as well as reflect the movement characteristics of moving objects is a core issue in the research field of trajectory prediction. Most of the existing trajectory prediction models are used to predict long sequential trajectory patterns according to the characteristics of historical trajectories, or the current locations of moving objects are integrated into spatio-temporal semantic scenarios to predict trajectories based on historical trajectories of moving objects. This survey summarizes the currently commonly-used trajectory prediction models and algorithms, involving different research fields. Firstly, the state-of-the-art works of multiple-motion trajectory prediction and the basic models of trajectory prediction are described. Secondly, the prediction models of different categories are summarized, including mathematical statistics, machine learning, filtering algorithm, as well as the representative methods in these research fields. Thirdly, the context awareness techniques are introduced, the definition of context awareness by different scholars from different research fields are described, the key technical points of context awareness techniques are presented, such as the different kinds of models on context awareness computing, context acquisition and context reasoning, and the different categories, filtering, storage and fusion of context awareness and their implementation methods are analyzed. The technical roadmap of multiple-motion-pattern trajectory prediction of moving objects with context awareness and the working mechanism of each task is introduced in detail. This survey presents the real-world application scenarios of context awareness techniques, for example, location recommendation, point of interest recommendation. By comparing them with traditional algorithms, the advantages and disadvantages of context awareness techniques in the aforementioned applications are discussed. The new methods for pedestrian trajectory prediction based on context awareness and long short-term memory (LSTM) techniques are introduced in detail. Lastly, the current problems and future trends of trajectory prediction and context awareness are summarized.