Abstract: Toroidal orbifolds represent the most fruitful and best understood backgrounds for string model building. When it comes to type IIA intersecting D6-branes, the most promising toroidal orbifold is undoubtedly T6/Z2xZ6 with discrete torsion. In this talk, we will discuss how to obtain on this background three generational chiral models without unwanted exotic matter charged under the Standard Model gauge group and present global supersymmetric extensions of the Standard Model. A second part of the talk will discuss deformations of the singularities and their implications for the global models.