Design space exploration is a long-standing focus in computational design research. Its three main threads are accounts of designer action, development of strategies for amplification of designer action in exploration and discovery of computational structures to support exploration. Chief amongst such structures is the design space - the network structure of related designs that are visited in an exploration process. There is relatively little research on design spaces to date. This paper sketches a partial account of the structure of both design spaces and research to develop them. It focuses largely on the implications of designers acting as explorers.