Although there have been some advances during in recent decades, the treatment of head and neck squamous cell carcinoma (HNSCC) remains challenging. Resistance is a major issue for various treatments that are used, including both the conventional standards of care (radiotherapy and platinum-based chemotherapy) and the newer EGFR and checkpoint inhibitors. In fact, all the non-surgical treatments currently used for HNSCC are associated with intrinsic and/or acquired resistance. Herein, we explore the cellular mechanisms of resistance reported in HNSCC, including those related to epigenetic factors, DNA repair defects, and several signaling pathways. This article discusses these mechanisms and possible approaches that can be used to target different pathways to sensitize HNSCC to the existing treatments, obtain better responses to new agents, and ultimately improve the patient outcomes.