SU(N) symmetric fermions on a lattice, which can be realized with alkaline earth atoms in optical lattices, have very promising prospects for realizing exotic states of matter. In the past decade substantial progress has been achieved in studying these systems in the strong coupling limit and integer filling, described by SU(N) Heisenberg models, using a variety of approaches. In this talk I will start with an overview of results for various SU(N) Heisenberg models obtained with infinite projected entangled pair states (iPEPS), and supported by linear flavor-wave theory, exact diagonalization, and variational Monte Carlo. The main part of this talk will be on the phase diagram of the SU(3) Hubbard model on the honeycomb lattice at 1/3 filling, which is considerably more challenging than the Heisenberg case. In the strongly interacting limit the ground state exhibits plaquette order. Upon decreasing the interaction strength a first-order transition is found at U/t = 7.2(2) into a dimerized, color-ordered state. This phase extends down to U/t = 4.5(5), at which the Mott transition occurs and the ground state becomes uniform. Finally, I will highlight recent developments in tensor network methods which will be useful for future studies of SU(N) models.