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The ability to predict, anticipate and reason about future outcomes is a key component of intelligent decision-making systems. In light of the success of deep learning in computer vision, deep-learning-based video prediction emerged as a promising research direction. Defined as a self-supervised learning task, video prediction represents a suitable framework for representation learning, as it demonstrated potential capabilities for extracting meaningful representations of the underlying patterns in natural videos. Motivated by the increasing interest in this task, we provide a review on the deep learning methods for prediction in video sequences. We firstly define the video prediction fundamentals, as well as mandatory background concepts and the most used datasets. Next, we carefully analyze existing video prediction models organized according to a proposed taxonomy, highlighting their contributions and their significance in the field. The summary of the datasets and methods is accompanied with experimental results that facilitate the assessment of the state of the art on a quantitative basis. The paper is summarized by drawing some general conclusions, identifying open research challenges and by pointing out future research directions.