I will survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes, with emphasis on the Cauchy problem. According to the BKL proposal generic singularities with non-stiff matter are space-like and oscillatory while in the presence of stiff matter or scalar fields the singularity is quiescent. I will discuss the picture that emerges from the BKL proposal and review some recent results on nonlinear stability and the Cauchy problem with rough initial data.