Global boundary conditions for elliptic first order differential operators on Riemannian manifolds are rather well understood. Bär-Strohmaier introduced APS-conditions for the Lorentzian Dirac-Operator on spacetimes with spacelike boundary, which was the starting point of the research on global boundary conditions in the context of Lorentzian manifolds. The increasing relevance of, for example, the anti-de Sitter spacetime in theoretical physics motivates us to also consider global boundary conditions in the context of spacetimes with timelike boundary. In this talk, I will give a brief introduction to globally hyperbolic manifolds with timelike boundary and the Lorentzian Dirac-Operator on these manifolds. Then, I will discuss global boundary conditions and the related Cauchy problems in this setting.