  QCD can be formulated using any gauge group. One particular interesting
choice is to replace SU(3) by the exceptional group G2. Conceptually, this
group is the simplest group with a trivial center. It thus permits to study the
conjectured relevance of center degrees of freedom for QCD. Practically, since
all its representation are real, it is possible to perform lattice simulations
for this theory also at finite baryon densities. It is thus an excellent
environment to test methods and to investigate general properties of gauge
theories at finite densities. We review the status of our understanding of
gauge theories with the gauge group G2, including Yang-Mills theory,
Yang-Mills-Higgs theory, and QCD both in the vacuum and in the phase diagram.
