Interaction effects in condensed matter systems with chiral quasiparticles at low energy are studied. A prominent example in the category of such systems is monolayer graphene, which has low energy massless Dirac excitations near some special points in the momentum space. We consider three generalized Dirac systems, which include ABC-stacked trilayer graphene, a superlattice of a gapped Dirac system decorated with charged impurities, and chromium dioxide (CrO2) bilayers. Interaction effects and interaction-induced phases are examined in these systems. For the ABC-stacked trilayer graphene, we calculate the renormalization properties of the chiral massless quasiparticles due to electron-electron interactions. Renormalization features of several physical observables are also studied, which may be measured in experiments. For the superlattice system of a two-dimensional gapped Dirac system with charged impurities, we show that this superlattice system can simulate SU(4) symmetric spin-orbital lattice models. We study the correlations of mid-gap bound states formed around the Coulomb impurities and propose the emergence of quantum spin-orbital liquids in this setup. In the third part, the focus is on the system of chromium dioxide bilayers, which also host Dirac quasiparticles at low energy. We investigate the possibility of forming chiral p+ip superconductivity in chromium dioxide bilayers.