Robust multi-agent trajectory prediction is essential for the safe control of robots and vehicles that interact with humans. Many existing methods treat social and temporal information separately and therefore fall short of modelling the joint future trajectories of all agents in a socially consistent way. To address this, we propose a new class of Latent Variable Sequential Set Transformers which autoregressively model multi-agent trajectories. We refer to these architectures as AutoBots. AutoBots model the contents of sets (e.g. representing the properties of agents in a scene) over time and employ multi-head self-attention blocks over these sequences of sets to encode the sociotemporal relationships between the different actors of a scene. This produces either the trajectory of one ego-agent or a distribution over the future trajectories for all agents under consideration. Our approach works for general sequences of sets and we provide illustrative experiments modelling the sequential structure of the multiple strokes that make up symbols in the Omniglot data. For the single-agent prediction case, we validate our model on the NuScenes motion prediction task and achieve competitive results on the global leaderboard. In the multi-agent forecasting setting, we validate our model on TrajNet. We find that our method outperforms physical extrapolation and recurrent network baselines and generates scene-consistent trajectories.