Based on the idea of the materiality of the gravitational field, two physical models of gravity are proposed: Model 1 – the equivalent scheme of gravistatics and Model 2 – the vacuum profile of withdrawals from the physical vacuum in the region of a black hole. Model 1 clearly illustrates the fundamental difference between electrostatic interaction and gravity. In particular, it confirmed the validity of the Mach principle, the presence of a double action of the gravitational field and the huge (but not infinite!) gravity propagation speed υg ~ 1069 m/s. Model 2 made it possible to distinguish between the phenomena of the expansion of the universe and the recession of galaxies, to understand their physical essence and to obtain Hubble's law. An important achievement of the model should be considered that the interpretation of these phenomena is based on the features of gravity and does not require the involvement of ideas about additional substances – dark matter and dark energy. The most important common achievement of the models is their ability to explain the gravitational spontaneous generation of the universe – the emergence of a metastable Metauniverse, within which a large number of universes simultaneously appear. This explanation involves the whole complex of features of gravity, emphasized by the models themselves. In particular, the spontaneous generation of the universe does not run into the problem of singularities and does not require far-fetched effects such as an inflationary stage of expansion or special vacuum states.