In calls for privacy by design (PBD), regulators and privacy scholars have investigated the richness of the concept of "privacy." In contrast, "design" in HCI is comprised of rich and complex concepts and practices, but has received much less attention in the PBD context. Conducting a literature review of HCI publications discussing privacy and design, this paper articulates a set of dimensions along which design relates to privacy, including: the purpose of design, which actors do design work in these settings, and the envisioned beneficiaries of design work. We suggest new roles for HCI and design in PBD research and practice: utilizing valuesand critically-oriented design approaches to foreground social values and help define privacy problem spaces. We argue such approaches, in addition to current "design to solve privacy problems" efforts, are essential to the full realization of PBD, while noting the politics involved when choosing design to address privacy. CCS CONCEPTS • Security and privacy → Human and societal aspects of security and privacy; • Social and professional topics → Computing / technology policy; • Human-centered computing → HCI design and evaluation methods.