Most recent successes on forecasting the people mo-tion are based on LSTM models andallmost recent progress hasbeen achieved by modelling the social interaction among peopleand the people interaction with the scene. We question the useof the LSTM models and propose the novel use of TransformerNetworks for trajectory forecasting. This is a fundamental switchfrom the sequential step-by-step processing of LSTMs to theonly-attention-based memory mechanisms of Transformers. Inparticular, we consider both the original Transformer Network(TF) and the larger Bidirectional Transformer (BERT), state-of-the-art on all natural language processing tasks. Our proposedTransformers predict the trajectories of the individual peoplein the scene. These are “simple” models because each personis modelled separately without any complex human-human norscene interaction terms. In particular, the TF modelwithoutbells and whistlesyields the best score on the largest and mostchallenging trajectory forecasting benchmark of TrajNet [1]. Ad-ditionally, its extension which predicts multiple plausible futuretrajectories performs on par with more engineered techniqueson the 5 datasets of ETH [2]+UCY [3]. Finally, we showthat Transformers may deal with missing observations, as itmay be the case with real sensor data. Code is available atgithub.com/FGiuliari/Trajectory-Transformer