We discuss results about inhomogeneous chiral phases, i.e. phases where in addition to chiral symmetry also translational symmetry is broken, in the $2+1$-dimensional Gross-Neveu model using the mean-field approximation. The phase diagram of the GN model is presented and the existence of inhomogeneous phases is ruled out. The non-existence of inhomogeneous phases will then be shown for a variety of Four-fermion and Yukawa models in 2+1 dimensions. Numerical minimizations of the effective action using two variants of naive fermions support our results.