The immune system functions to defend the organism against infectious microorganisms but also against transformed cells. This key role of the immune system, in particular cancer-specific T cells, in eliminating cancer cells is compromised by various immune escape strategies employed by cancer cells and the cancer microenvironment. Here, we review the current knowledge about the immune escape mechanisms of cancer and the attempts to reconstitute cancer-specific immunity by using checkpoint inhibitors in head and neck squamous cell carcinoma. We discuss the different options of immune therapy based on a mechanistic understanding of the relevance of co-inhibitory signaling, regulatory T cells, and myeloid-derived suppressor cells. A thorough mechanistic understanding of cancer immune escape mechanisms and their presence in the individual patient is required in order to design effective multicomponent immune therapies in the future.