One conjecture for the still highly disputed QCD phase diagram is that at sufficient baryon densities inhomogeneous phases might be preferred. As this region is still well out of reach for full lattice-QCD simulations, there is great on-going effort to further substantiate this claim in fermionic toy models and effective theories. I will discuss the recent advances with focus on our own results on (chiral) Gross-Neveu models in lower dimensions.