On the global initial value problem and the issue of singularities

In the first part of the paper we discuss what is known at present about th e global initial value problem for the vacuum Einstein equations with gener al asymptotically flat initial data. We then give precise formulations of c osmic censorship conjectures. We also point out analogies with fluid dynami cs and discuss possibilities suggested by these analogies. In the second pa rt I discuss my work on the spherically symmetric Einstein equations with a real massless scalar field as the material model. I give an outline of the approach which has led to the proof of the conjectures in this context.