On September 14, 2015, the LIGO interferometers captured a gravitational wave (GW) signal from two merging black holes (BHs), opening the era of GW astrophysics. Five BH mergers have been reported so far, three of them involving massive BHs (>30M_⊙). According to stellar evolution models, such massive BHs can originate from massive relatively metal-poor stars. Alternatively, gravitational instabilities in the early Universe were claimed to produce BHs in this mass range. The formation channels of merging BH binaries are still an open question: a plethora of uncertainties affect the evolution of massive stellar binaries (e.g. the process of common envelope) and their dynamics. This review is intended to discuss the open questions about BH binaries, and to present the state-of-the-art knowledge about the astrophysics of black holes for non-specialists, in light of the first LIGO detections