Immune checkpoint inhibitors, including those targeting CTLA-4/B7 and the PD-1/PD-L1 inhibitory pathways, are now available for clinical use in cancer patients, with other interesting checkpoint inhibitors being currently in development. Most of these have the purpose to promote adaptive T cell-mediated immunity against cancer. Here, we review another checkpoint acting to potentiate the activity of innate immune cells towards cancer. This innate immune checkpoint is composed of what has become known as the 'don't-eat me' signal CD47, which is a protein broadly expressed on normal cells and often overexpressed on cancer cells, and its counter-receptor, the myeloid inhibitory immunoreceptor SIRPα. Blocking CD47-SIRPα interactions has been shown to promote the destruction of cancer cells by phagocytes, including macrophages and neutrophils. Furthermore, there is growing evidence that targeting of the CD47-SIRPα axis may also promote antigen-presenting cell function and thereby stimulate adaptive T cell-mediated anti-cancer immunity. The development of CD47-SIRPα checkpoint inhibitors and the potential side effects that these may have are discussed. Collectively, this identifies the CD47-SIRPα axis as a promising innate immune checkpoint in cancer, and with data of the first clinical studies with CD47-SIRPα checkpoint inhibitors expected within the coming years, this is an exciting and rapidly developing field.