The ability to forecast human motion, called ``human trajectory forecasting", is a critical requirement for mobility applications such as autonomous driving and robot navigation. Humans plan their path taking into account what might happen in the future. Similarly, the decision-making algorithm of autonomous systems should predict how their environment will evolve in the future. This thesis focuses on developing deep learning methods for forecasting human motion. In the first part of this thesis, we tackle the fundamental challenges of social interaction modelling and multimodality. Social interactions dictate how the motion of a human is affected by others. Current deep learning methods often struggle to model these interactions between trajectory sequences. To promote interaction-awareness in forecasting models, we develop a training paradigm that explicitly focuses on samples that undergo interactions and incorporates model uncertainty. Furthermore, we build a taxonomy of existing interaction encoders and propose an optimal design that is robust to the real-world noise. In addition to modelling interactions, a good trajectory forecasting model must account for the multimodal nature of the prediction, i.e., the possibility of having multiple plausible futures given the past observations. To tackle multimodality, we present a socially-aware generative adversarial network that leverages recent advances in sequence modelling, and has the ability to model the temporal evolution of social interactions. Furthermore, we develop a collaborative sampling technique that refines the bad generated predictions at test time. In the second part of this thesis, we focus on two challenges specific to the real-world deployment of forecasting models: interpretability and adaptability. While neural networks have the capacity to learn complex interactions, it is difficult to understand the reason behind their predictions. Thus, we develop a framework that combines the interpretability of the classical models with the predictive power of neural networks. With regards to adaptability, existing deep forecasting models suffer from inferior performance when they encounter novel scenarios. We develop a strategy to adapt a pre-trained forecasting model to a target domain using limited samples. In particular, we introduce motion style adapters that identify and adjust the target domain-specific features. Throughout this thesis, experiments on synthetic and real-world forecasting datasets validate the effectiveness of our proposed methods.