The zero-pressure gas dynamics system in nonconservative form is one of the most important models for the formation and evolution of large-scale structures in the universe. It consists of the multidimensional inviscid Burgers equation for the velocity component and the continuity equation for the density component. The main open question concerns finding the appropriate regularity space for the velocity component and the weak formulation of the concept of solution for the associated Cauchy problem. Not much is known on the well-posedness of the Cauchy problem except for very special type of initial conditions. Here we review some of the main works on this system.