Preclinical data suggest that head and neck squamous cell carcinomas (HNSCC) may evade immune surveillance and induce immunosuppression. One mechanism of immune evasion involves the expression of programmed death ligand-1 (PD-L1) in tumor and immune cells, which is, to date, the only biomarker routinely used in clinical practice to select patients with advanced HNSCCs more likely to benefit from anti-PD-1 therapy. Nonetheless, PD-L1 expression alone incompletely captures the degree of sensitivity of HNSCCs to PD-1 inhibitors. Most patients exposed to anti-PD-1 antibodies do not respond to therapy, suggesting the existence of mechanisms of de novo resistance to immunotherapy. Furthermore, patients that initially respond to PD-1 inhibitors will eventually develop acquired resistance to immunotherapy through mechanisms that have not yet been completely elucidated. In this article, we will provide an overview of the immune landscape of HNSCCs. We will briefly describe the clinical activity of inhibitors of the PD-1/PD-L1 axis in this disease, as well as biomarkers of benefit from these agents that have been identified so far. We will review pre-clinical and clinical work in cancers in general, and in HNSCCs specifically, that have characterized the mechanisms of de novo and acquired resistance to immunotherapy. Lastly, we will provide insights into novel strategies under investigation to overcome resistance to immune checkpoint inhibitors.