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A domain-specific language (DSL) design space describes a collection of related languages via a series of, often orthogonal, dimensions. While PL and HCI researchers have independently developed methods for working with design spaces, the communities have yet to fully benefit from each others' insights. In pursuit of new approaches informed by both PL and HCI, we first review existing approaches researchers employ to conceptualize, develop, and use design spaces in DSL design across the two disciplines. For example, HCI researchers, when developing interfaces backed by DSLs, often treat the design process as core to their research contributions and theory-building. In PL, researchers have explored formal approaches to design spaces that help automate design space exploration and provide powerful conceptual clarity to language design tradeoffs. We then discuss areas where the two fields share common methods and highlight opportunities for researchers to combine knowledge across PL and HCI.