The 2020 Nobel Prize in Physics has been awarded to Roger Penrose, Reinhard Genzel and Andrea Ghez for their discoveries related to black holes. One half of the Prize has been awarded to Roger Penrose “for the discovery that black hole formation is a robust prediction of the general theory of relativity”, the other half jointly to Reinhard Genzel and Andrea Ghez “for the discovery of a supermassive compact object at the center of our galaxy”. In this article, we will briefly review the relevant background and historical developments of the field, followed by introducing their main contributions. The first solution to Einstein’s field equation shows the existence of singularity and the black hole. But this solution is based on an assumption of spherical symmetry. By abandoning this assumption, Penrose for the first time has shown that the singularity still exists and the black hole is a robust prediction of the general relativity. The critical concept Penrose introduced was trapped surface, a closed two-dimensional surface whose light rays are perpendicular to the surface and converging towards the future. Penrose showed that no matter what disturbances the star encounters during collapse and whether the star is spherically symmetrical or not, the capture surface always exists, which would mean that the gas would collapse inexorably toward the center to form a singularity under general relativity. This work is widely regarded as the most important research achievement in the field of general relativity since Einstein. We now know that black holes are widespread in the universe, with at least a hundred million small black holes in a galaxy like the Milky Way which are evolved by stars; and that almost every galaxy has an intergalactic supermassive black hole at its center. In addition to quasars, many other important astronomical observations are caused by black holes. Penrose’s work has opened up a new era of astronomical and astrophysical research. Reinhard Genzel and Andrea Ghez have tested this prediction by precisely measuring the orbits and radial velocities of stars surrounding a supermassive compact object located at the center of our galaxy. For more than 20 years, they have been dedicated to observing the movements of stars at the center of the Milky Way. To begin with, being able to identify individual stars, even if they are at the center of our own Milky Way galaxy, requires extremely high telescope resolution. Infrared photons with longer wavelengths can pass through the interstellar dust. Both groups therefore observed at near-infrared wavelengths. Another difficulty comes from the wobble of the Earth’s atmosphere, turbulence. The turbulent flow reduces the quality of the telescope’s image of the star. The observation difficulties were eventually overcome by a revolutionary new technology called adaptive optics. Invented in 1953, the technique was successfully used on telescopes used by two teams in the early 2000s. With these innovations in ideas and techniques, they find that the observational results are fully compatible with the theoretical prediction of a black hole. Several recent other scientific awards on black hole studies are also briefly introduced.