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We present this Collection of research, review and comment from Nature Research to celebrate the award of the 2020 Nobel Prize in Physics to Roger Penrose “for the discovery that black hole formation is a robust prediction of the general theory of relativity” and to Reinhard Genzel and Andrea Ghez “for the discovery of a supermassive compact object at the centre of our Galaxy”. Their combined work cemented the existence of black holes and paved the way for the Event Horizon Telescope and gravitational wave detectors.