Abstract: 3-manifolds which are spacelike slices of flat spacetimes, I and II. We will be concerned with spacetimes of the form M^3 x R, where M^3 is a closed connected 3-manifold, the slices M^3 x t are spacelike, and the spacetime metric is flat. The main result determines exactly which M^3's arise -- roughly M is hyperbolic or else has a finite cover of the form (surface x S^1). The first talk will be devoted primarily to surveying what is known about classifying closed 3-manifolds. The second talk will sketch the proof of the main theorem, which relies on powerful `homotopy equivalence => homeomorphism' results for 3-manifolds due to Waldhausen, Scott, Mess, Gabai, and others