Head and neck squamous cell carcinoma (HNSCC) is a very heterogeneous cancer with a poor overall response to therapy. One of the reasons for this therapy resistance could be cancer stem cells (CSCs), a small population of cancer cells with self-renewal and tumor-initiating abilities. Tumor cell heterogeneity represents hurdles for therapeutic elimination of CSCs. Different signaling pathway activations, such as Wnt, Notch, and Sonic-Hedgehog (SHh) pathways, lead to the expression of several cancer stem factors that enable the maintenance of CSC features. Identification and isolation of CSCs are based either on markers (CD133, CD44, and aldehyde dehydrogenase (ALDH)), side populations, or their sphere-forming ability. A key challenge in cancer therapy targeting CSCs is overcoming chemotherapy and radiotherapy resistance. However, in novel therapies, various approaches are being employed to address this hurdle such as targeting cell surface markers, other stem cell markers, and different signaling or metabolic pathways, but also, introducing checkpoint inhibitors and natural compounds into the therapy can be beneficial.