In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of the broader phase diagram. In systems with both spin and orbital (or valley) degrees of freedom, SU(4)-symmetric models can serve as such a starting point. In this talk I will discuss SU(4) quantum antiferromagnets on the triangular lattice, that arise from Mott-insulating phases of fermions with four flavors. I will consider different fillings of the SU(4) fermions, which lead to different representations of SU(4) on each site. First, I will discuss the case of two fermions per site (i.e. half-filling), which corresponds to the 6-dimensional representation of SU(4). I will argue that in this case, the low energy properties of the model can be captured by an effective dimer model. I will then present exact diagonalization studies of the dimer model indicating that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. In the second part of my talk, I will turn to the case of a single fermion per site, corresponding to the fundamental representation of SU(4). Based on numerical simulations using the density matrix renormalization group (DMRG) method, supported by field-theoretical arguments, I will provide evidence for a gapless liquid with an emergent Fermi surface in the ground state of the system.