We analyze, via first principles molecular dynamics, the structural and electronic properties of water close to and above the critical point. Contrary to the ordinary liquid state, at supercritical conditions the hydrogen bond network is destabilized to various extents and the continuous breaking and reformation of hydrogen bonded structures allow large density and dipole fluctuations that, in turn, can significantly affect the dielectric properties of the solvent. Close to the critical point, where the density is very low, small clusters, mainly dimers and trimers, are the dominant features, but many molecules exhibit no H-bond. On the other hand, at higher densities, more extended structures appear, but still a continuous network cannot form. In both cases, H-bond configurations that are anomalous with respect to the normal liquid phase appear. These features strongly affect the solvent properties of supercritical water with respect to those of ambient water. They most likely vary continuously as a function of temperature, pressure and density and, hence, can be tuned to optimize the desired chemical process.