This chapter explains how the researchers of the Event Horizon Telescope Collaboration were able to obtain the first picture of a black hole through radio-astronomical observations. In particular, we first describe the technological strategies that have been exploited in order to obtain a record-high angular resolution. We will also discuss the theoretical aspects that have allowed the collaboration to model the dynamics of the plasma falling onto the black and to produce a large database of synthetic images potentially describing an accreting supermassive black hole. The chapter reviews how the comparison between the theoretical images and the observations has allowed us to deduce the presence of a supermassive black hole with a mass of 6 billion solar masses in the very heart of the giant galaxy M87. The chapter will also summarise the lessons that have been learnt from this epochal achievement and the questions that are still left unanswered about black holes and gravity in the strongest regimes.

The Schwarzschild black holes discussed in Chapter 12 are not the most general black hole spacetimes predicted by general relativity. They are simple objects – exactly spherically symmetric and characterized by a single parameter, the total mass. Remarkably, the most general stationary black hole solutions of the vacuum Einstein equation are not much more complicated. They are described by the family of geometries discovered by Roy Kerr in 1963, and are called Kerr black holes. Members of the family depend on just two parameters – the total mass and total angular momentum. Kerr black holes are the rotating generalizations of the Schwarzschild black hole. This chapter gives an elementary introduction to their properties.