Lattice simulations of QCD-like theories at non-zero density

One way of avoiding the complex action problem in lattice QCD at non-zero density is to simulate QCD-like theories with a real action, such as two-colour QCD. The symmetries of two-colour QCD with quarks in the fundamental and in the adjoint representation are described, and the status of lattice simulations is reviewed, with particular emphasis on comparison with predictions from chiral perturbation theory. Finally, we discuss how the lessons from two-colour QCD may be carried over to physical QCD.