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.

This chapter gives a brief overview of observational astronomy, using optical instruments and other wavelengths. We present a general formula for the increase in the limiting magnitude resulting from an increased telescope aperture. For light of particular wavelength, the diffraction from a telescope with a specific diameter sets a fundamental limit to the smallest possible angular separation that can be resolved.