Immunotherapy revolutionized cancer treatment but has yet to elicit durable responses in the majority of patients with head and neck squamous cell carcinoma (HNSCC). HNSCC is generally characterized by a high tumor mutational burden, which has translated to a large neoantigen load that could prime the immune system to recognize and eliminate malignant cells. Studies are increasingly showing, however, that HNSCC is an "immune desert" tumor that can hijack multiple parts of the tumor immunity cycle in order to evade immune recognition and suppress immune system activation. Herein we will review how HNSCC tumors modulate their architecture, cellular composition, and cytokine milieu to maximize immunosuppression; as well as relevant therapeutic opportunities and emerging issues facing the field of HNSCC immuno-oncology.