The articles in this special section focus on long term human motion prediction. This represents a key ability for advanced autonomous systems, especially if they operate in densely crowded and highly dynamic environments. In those settings understanding and anticipating human movements is fundamental for robust long-term operation of robotic systems and safe human-robot collaboration. Foreseeing how a scene with multiple agents evolves over time and incorporating predictions in a proactive manner allows for novel ways of planning and control, active perception, or humanrobot interaction. Recent planning and control approaches use predictive techniques to better cope with the dynamics of the environment, thus allowing the generation of smoother and more legible robot motion. Predictions can be provided as input to the planning or optimization algorithm (e.g. as a cost term or heuristic function), or as additional dimension to consider in the problem formulation (leading to an increased computational complexity). Recent perception techniques deeply interconnect prediction modules with detection, segmentation and tracking, to generally increase the accuracy of different inference tasks, i.e. filtering, predicting. As also indicated by some of the scientific works accepted in this special issue, novel deep learning architectures allow better interleaving of the aforementioned units.