Time is deeply woven into how people perceive, and communicate about the world. Almost unconsciously, we provide our language utterances with temporal cues, like verb tenses, and we can hardly produce sentences without such cues. Extracting temporal cues from text, and constructing a global temporal view about the order of described events is a major challenge of automatic natural language understanding. Temporal reasoning, the process of combining different temporal cues into a coherent temporal view, plays a central role in temporal information extraction. This article presents a comprehensive survey of the research from the past decades on temporal reasoning for automatic temporal information extraction from text, providing a case study on the integration of symbolic reasoning with machine learning-based information extraction systems.