[en] In this work, we have investigated three-dimensional relativistic fermion systems from the perspective of the renormalization group (RG). We have classified these systems with respect to their symmetry and have focussed in particular on the chiral Gross-Neveu (GN) model and the Thirring model with U_L(N_L) x U_R(N_R) and U(2N_f) symmetry, respectively. While perturbatively nonrenormalizable, we have shown that these models can indeed be defined nonperturbatively, exhibiting the same amount of universality as any perturbatively renormalizable field theory. We have generalized the 3d chiral GN model by allowing for a different number of left- and righthanded fermion flavors, reminiscent of the Higgs-Yukawa sector of the particle-physics' standard model (where N_L=2 and N_R=1). By means of the functional RG in terms of the Wetterich equation, we have been able to identify a non-Gaussian fixed point for any N_L element of [1,∞] with N_R=1, corresponding to a second-order chiral phase transition. We have provided quantitative predictions for the critical behavior in terms of the universal critical exponents ν, η_φ, η_ψ, and ω. Our results support the conjecture that in the N_L → ∞ limit our U_L(N_L) x U_R(1) is in the universality class of the purely bosonic O(2N_L) model, in which case the critical exponents are known to very high accuracy. For N_L=1, our model coincides with the usual one-flavor chiral GN model. In this sense, for intermediate N_L our models ''interpolate'' between the purely bosonic O(2N_L) model and the purely fermionic GN model with continuous chiral symmetry. Beyond these two limits, our models define new universality classes, the critical behavior of which has previously been unknown. Within a simple truncation of the effective action in terms of solely fermionic degrees of freedom, we have obtained a unified picture of the class of maximally symmetric 3d fermion systems, exhibiting U(2N_f) chiral and a set of discrete symmetries. The Thirring and the NJL model in three dimensions are of this type and we have shown that both are in fact in the same universality class, governed by the same interacting fixed point. We have also identified another interacting fixed point, governing the discrete symmetry breaking of the 3d GN model in the irreducible representation. We have advanced our truncation by allowing for composite bosonic degrees of freedom by means of the bosonization technique. For a quantitatively reliable investigation of the competition between the different condensation channels, we have shown that it is necessary to employ a formulation which does not suffer from the Fierz ambiguity. We have done this by performing the Hubbard-Stratonovich transformation at each RG step in terms of dynamical bosonization. As a function of N_f for fixed over-critical coupling, we have found a phase transition at a critical flavor number N"c"r_f≅5.1(7), which is governed by the IR dynamics of the system. By contrast, the phase transformation as a function of the b are coupling for fixed N_f< N_f"c"r is determined by the RG flow in the UV regime. For the latter, our RG approach allows to yield very precise predictions; we have computed in detail the values of the universal critical exponents ν, η_φ, and ω as a function of N_f. For N_f=2, we have (independently of our results on ν and η_φ) also computed the exponents β and γ.