CD47 is a ubiquitously expressed cell surface glycoprotein that functions as a signaling receptor for thrombospondin-1 and as the counter-receptor for signal regulatory protein-α (SIRPα). Engaging SIRPα on macrophages inhibits phagocytosis, and CD47 thereby serves as a physiological marker of self. However, elevated CD47 expression on some cancer cells also protects tumors from innate immune surveillance and limits adaptive antitumor immunity via inhibitory SIRPα signaling in antigen-presenting cells. CD47 also mediates inhibitory thrombospondin-1 signaling in vascular cells, T cells, and NK cells, and blocking inhibitory CD47 signaling on cytotoxic T cells directly increases tumor cell killing. Therefore, CD47 functions as an innate and adaptive immune checkpoint. These findings have led to the development of antibodies and other therapeutic approaches to block CD47 functions in the tumor microenvironment. Preclinical studies in mice demonstrated that blocking CD47 can limit the growth of hematologic malignancies and solid tumors and enhance the efficacy of conventional chemotherapy, radiation therapy, and some targeted cancer therapies. Humanized CD47 antibodies are showing promise in early clinical trials, but side effects related to enhanced phagocytic clearance of circulating blood cells remain a concern. Approaches to circumvent these include antibody preloading strategies and development of antibodies that recognize tumor-specific epitopes of CD47, SIRPα antibodies, and bivalent antibodies that restrict CD47 blockade to specific tumor cells. Preclinical and clinical development of antibodies and related biologics that inhibit CD47/SIRPα signaling are reviewed, including strategies to combine these agents with various conventional and targeted therapeutics to improve patient outcome for various cancers.