I review the properties of the NJL model in 2+1 dimensions with a baryon chemical potential $\mu$. At zero temperature the model undergoes a first order chiral phase transition. Quantitative results of the end of the first order line in the $(\mu, T)$ plane are given. The universality of the second order transition line is that of the classical 2d spin model in accordance with the dimensional reduction scenario. I also discuss the particle interaction due to scalar exchange to leading order in $1/N_f$ in the cold-dense phase. Simulation results for fermion and meson dispersion relations and meson wavefunctions show qualitative agreement with analytic predictions.