Grand Unification in the Heterotic Brane World

The compactification of the heterotic string on six-dimensional orbifolds is reviewed. Some important technical aspects of their construction are clarified and new parameters, called generalized discrete torsion, are introduced and related to the torsionless construction. Furthermore, a systematic search for MSSM-like models is performed in the context of Z6-II orbifolds, addressing questions like the identification of a supersymmetric vacuum with a naturally small mu-term and proton decay. Finally, the blow-up of Z3 singularities is discussed in the local and in the global case - also in the presence of Wilson lines. This procedure is exemplified with the resolution of a Z3 MSSM candidate.