The talk will review recent results related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g. graphene and graphene-like systems. These liquids are characterized by gapless bands, strong electron-electron interactions and emergent Lorentz invariance deep in the infra-red. We address a number of important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) as well as high-energy physics. We shall consider in particular the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation.