We present the second edition of OpenEDS dataset, OpenEDS2020, a novel dataset of eye-image sequences captured at a frame rate of 100 Hz under controlled illumination, using a virtual-reality head-mounted display mounted with two synchronized eye-facing cameras. The dataset, which is anonymized to remove any personally identifiable information on participants, consists of 80 participants of varied appearance performing several gaze-elicited tasks, and is divided in two subsets: 1) Gaze Prediction Dataset, with up to 66,560 sequences containing 550,400 eye-images and respective gaze vectors, created to foster research in spatio-temporal gaze estimation and prediction approaches; and 2) Eye Segmentation Dataset, consisting of 200 sequences sampled at 5 Hz, with up to 29,500 images, of which 5% contain a semantic segmentation label, devised to encourage the use of temporal information to propagate labels to contiguous frames. Baseline experiments have been evaluated on OpenEDS2020, one for each task, with average angular error of 5.37 degrees when performing gaze prediction on 1 to 5 frames into the future, and a mean intersection over union score of 84.1% for semantic segmentation. As its predecessor, OpenEDS dataset, we anticipate that this new dataset will continue creating opportunities to researchers in eye tracking, machine learning and computer vision communities, to advance the state of the art for virtual reality applications. The dataset is available for download upon request at this http URL.