Phase diagrams of exceptional and supersymmetric lattice gauge theories In this work different strongly coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non trivial centre symmetry as for instance SU(3) Yang Mills theory confinement is intimately related to the centre of the gauge group and the Polyakov loop serves as an order parameter for confinement. In QCD this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons baryons and glueballs at low temperatures and small densities suggesting that centre symmetry is not responsible for the phenomenon of confinement.