High resolution imaging of protostellar discs through ALMA at sub-mm wavelengths and through extreme adaptive optics systems, such as SPHERE, in the near infrared, is revolutionizing our view of the earliest phases of planet formation. Young protostellar discs reveal a wealth of substructures in the form of spiral arms, gaps and rings, horseshoe features and warped structures. On the one hand, such structures are the signposts of planet formation, being likely shaped by the gravitational interaction of the disc with newly born planets. On the other hand, their presence strongly affects the dynamics of dust grains in the disc, which are the main ingredient for the formation of rocky and gaseous planets. In this talk, I will discuss the new perspectives opened by such discoveries in the theoretical description of the dynamics of gas and dust in a young, planet forming disc. I will show our recent hydrodynamical simulations of the coupled gas and dust dynamics in protostellar discs, obtained with the SPH code PHANTOM, in order to describe the features observed in high resolution imaging and in order to identify new dynamical processes that are likely at work in these systems.