  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.
