Head and neck squamous cell carcinoma (HNSCC) is one of the most aggressive and heterogeneous groups of human neoplasms. HNSCC is characterized by high morbidity, accounting for 3% of all cancers, and high mortality with ~1.5% of all cancer deaths. It was the most common cancer worldwide in 2020, according to the latest GLOBOCAN data, representing the seventh most prevalent human malignancy. Despite great advances in surgical techniques and the application of modern combinations and cytotoxic therapies, HNSCC remains a leading cause of death worldwide with a low overall survival rate not exceeding 40–60% of the patient population. The most common causes of death in patients are its frequent nodal metastases and local neoplastic recurrences, as well as the relatively low response to treatment and severe drug resistance. Much evidence suggests that the tumour microenvironment (TME), tumour infiltrating lymphocytes (TILs) and circulating various subpopulations of immunocompetent cells, such regulatory T cells (CD4+CD25+Foxp3+Tregs), cytotoxic CD3+CD8+ T cells (CTLs) and CD3+CD4+ T helper type 1/2/9/17 (Th1/Th2/Th9/Th17) lymphocytes, T follicular helper cells (Tfh) and CD56dim/CD16bright activated natural killer cells (NK), carcinoma-associated fibroblasts (CAFs), myeloid-derived suppressor cells (MDSCs), tumour-associated neutrophils (N1/N2 TANs), as well as tumour-associated macrophages (M1/M2 phenotype TAMs) can affect initiation, progression and spread of HNSCC and determine the response to immunotherapy. Rapid advances in the field of immuno-oncology and the constantly growing knowledge of the immunosuppressive mechanisms and effects of tumour cancer have allowed for the use of effective and personalized immunotherapy as a first-line therapeutic procedure or an essential component of a combination therapy for primary, relapsed and metastatic HNSCC. This review presents the latest reports and molecular studies regarding the anti-tumour role of selected subpopulations of immunocompetent cells in the pathogenesis of HNSCC, including HPV+ve (HPV+) and HPV−ve (HPV−) tumours. The article focuses on the crucial regulatory mechanisms of pro- and anti-tumour activity, key genetic or epigenetic changes that favour tumour immune escape, and the strategies that the tumour employs to avoid recognition by immunocompetent cells, as well as resistance mechanisms to T and NK cell-based immunotherapy in HNSCC. The present review also provides an overview of the pre- and clinical early trials (I/II phase) and phase-III clinical trials published in this arena, which highlight the unprecedented effectiveness and limitations of immunotherapy in HNSCC, and the emerging issues facing the field of HNSCC immuno-oncology.