This paper describes the MediaEval 2021 Predicting Media Memorability task. After first being proposed at MediaEval 2018, the Predicting Media Memorability task is in its 4th edition this year, as the prediction of short-term and long-term video memorability remains a challenging task. This year, two datasets of videos are used: first, as in the 2020 task, a subset of the TRECVid 2019 Video-to-Text dataset; second, the Memento dataset has been added to the task in order to provide opportunities to explore cross-dataset generalisation. In this paper we describe the 2021 Predicting Media Memorability task, including its main characteristics, the ground truth datasets, evaluation metrics, and the requirements for participants' run submissions.