The immune system evolved for adequate surveillance and killing of pathogens while minimizing host damage, such as due to chronic or exaggerated inflammation and autoimmunity. This is achieved by negative regulators and checkpoints that limit the magnitude and time course of the immune response. Tumor cells often escape immune surveillance and killing. Therefore, disrupting the brakes built into the immune system should effectively boost the anticancer immune response. The success of anti-CTLA4, anti-PD-1 and anti-PD-L1 have firmly established this proof of concept. Since the response rate of anti-CTLA4, anti-PD-1 and anti-PD-L1 is still limited, there is an intense effort for the identification of new targets and development of approaches that can expand the benefits of immunotherapy to a larger patient pool. Additional T cell checkpoints are obvious targets; however, here we focus on the unusual suspects—cells that function to initiate and guide T cell activity. Innate immunity is both an obligate prerequisite for the initiation of adaptive immune responses and a requirement for the recruitment of activated T cells to the site of action. We discuss some of the molecules present in innate immune cells, including natural killer cells, dendritic cells, macrophages, myeloid-derived suppressor cells, endothelial cells and stromal cells, that can activate or enhance innate immune cell functions, and more importantly, the inhibitors or checkpoints present in these cells that restrain their functions. Boosting innate immunity, either by enhancing activator functions or, preferably, by blocking the inhibitors, may represent a new anticancer treatment modality or at least function as adjuvants to T cell checkpoint inhibitors.