Pedestrian trajectory prediction is one of the main concerns of computer vision problems in the automotive industry, especially in the field of advanced driver assistance systems. The ability to anticipate the next movements of pedestrians on the street is a key task in many areas, e.g., self-driving auto vehicles, mobile robots or advanced surveillance systems, and they still represent a technological challenge. The performance of state-of-the-art pedestrian trajectory prediction methods currently benefits from the advancements in sensors and associated signal processing technologies. The current paper reviews the most recent deep learning-based solutions for the problem of pedestrian trajectory prediction along with employed sensors and afferent processing methodologies, and it performs an overview of the available datasets, performance metrics used in the evaluation process, and practical applications. Finally, the current work exposes the research gaps from the literature and outlines potential new research directions.