Head and neck cancer (HNC) entails a heterogenous neoplastic disease that arises from the mucosal epithelium of the upper respiratory system and the gastrointestinal tract. It is characterized by high morbidity and mortality, being the eighth most common cancer worldwide. It is believed that the mesenchymal/stem stromal cells (MSCs) present in the tumour milieu play a key role in the modulation of tumour initiation, development and patient outcomes; they also influence the resistance to cisplatin-based chemotherapy, the gold standard for advanced HNC. MSCs are multipotent, heterogeneous and mobile cells. Although no MSC-specific markers exist, they can be recognized based on several others, such as CD73, CD90 and CD105, while lacking the presence of CD45, CD34, CD14 or CD11b, CD79α, or CD19 and HLA-DR antigens; they share phenotypic similarity with stromal cells and their capacity to differentiate into other cell types. In the tumour niche, MSC populations are characterized by cell quiescence, self-renewal capacity, low reactive oxygen species production and the acquisition of epithelial-to-mesenchymal transition properties. They may play a key role in the process of acquiring drug resistance and thus in treatment failure. The present narrative review examines the links between MSCs and HNC, as well as the different mechanisms involved in the development of resistance to current chemo-radiotherapies in HNC. It also examines the possibilities of pharmacological targeting of stemness-related chemoresistance in HNSCC. It describes promising new strategies to optimize chemoradiotherapy, with the potential to personalize patient treatment approaches, and highlights future therapeutic perspectives in HNC.