Some recent progress toward a general theory of process synthesis is reviewed. The discussion is centered around attempts to understand what F. J. M. Horn called the attainable region-roughly, the full set of outcomes (in some suitable state space) that might be realized from all possible designs within a broad class. The boundary of the attainable region is of special importance because it carries information about the outermost limits of what can be realized. We consider two major problems: the pure reactor synthesis problem, in which one tries to assess what might be attained from a specified feed in all steady-state processes that involve only reaction and mixing, and the reactor-separator synthesis problem, in which one tries to assess the full set of effluents attainable in broadly constrained processes when separators are also brought into play. For the pure reactor synthesis problem, we review how one can say a great deal-in remarkably specific quantitative terms-about designs of classical reactors that shape the attainable region's boundary, even when that boundary is unknown. At the same time, we indicate why these very same results, however striking, point to serious obstacles along the road to future progress. The reactor-separator synthesis problem has a brighter outlook. For the purpose of finding outer bounds on the set of effluents attainable from all possible constraint-consistent steady-state designs, the Continuous Flow Stirred Tank Reactor (CFSTR) Equivalence Principle reduces the bewildering spectrum of reactor configurations that need be considered (including exotic, unimagined ones) to a surprisingly narrow class: those consisting of a small number of CFSTRs, the number depending in a simple way on the number of independent chemical reactions. To the extent that one can realize arbitrary separations, the principle serves to provide exact bounds on the set of effluents attainable from all steady-state constraint consistent reactor-separator designs.