The black hole X-ray binary V404 Cyg entered an outburst phase on 2015 June 15 after 26 years of X-ray quiescence. Its activity was monitored at all wavelengths by virtually all the ground and space based facilities that could observe the source. This produced the largest multi-wavelength dataset on an active black hole X-ray transient. Here we focus on the X-ray monitoring campaign we carried out with the INTEGRAL and Swift satellites. We briefly summarize the results that we obtained from the observation of the most active phase of the outburst and we will describe our understanding of the source in the context of what it is known about accreting stellar mass and super-massive black holes. The results of time-resolved spectroscopy revealed that while the soft X-ray spectra extracted from Swift data reveal the effects of very variable, high columndensity material obscuring the source, the hard X-ray spectra extracted from INTEGRAL are most sensitive the the source intrinsic (i.e. accretion driven) changes. Our results suggest that the inner part of the accretion flow in V404 Cyg is inflated into a so-called slim disk that hides the innermost regions of the flow, but also produces a cold, inhomogeneous, high-density outflow that introduces the high-absorption and fast spectral variability. We argue that the black hole in V404 Cyg might have been accreting erratically or even continuously at Eddington/Super-Eddington rates, while being partly or completely obscured. We therefore conclude that the part or even all of the flaring behaviour of the source might have not been accretion-driven, but rather the result of the covering/unveiling of the extremely bright source hidden within the system.