Compact objects and Black Holes: Nobel Prize for Physics 2020

The Nobel Prize in Physics 2020 has been divided, one half awarded to Roger Penrose for the discovery that black hole formation is a robust prediction of the general theory of relativity. and the other half jointly to Reinhard Genzel and Andrea Ghez for the discovery of a supermassive compact object at the centre of our galaxy. Here we describe their work and put it in historical context and discuss specific advances that have been rewarded.