Block's paper lays out some of the conceptual territory surrounding consciousness. He begins with the idea Nagel discusses and adds three further concepts. The first two of these--"phenomenal" and "access" consciousness--receive the bulk of his attention; but all four are worth thinking about, and we should spend some time discussing each.
That said, we are likely to spend most of our time as Block does, in talking about the relation between phenomenal and access consciousness. So be sure to give special attention to those concepts, to the relative ability of the various views of the mind we've seen to accommodate each of them, and to the examples Block offers to distinguish them.