Despite refinements to diagnostic and therapeutic approaches over the last two decades, the outcome of patients with head and neck squamous cell carcinoma (HNSCC) has not shown substantial improvements, especially regarding those with advanced-stage disease. Angiogenesis is believed to be a turning point in the development of solid tumors, being a premise for mass growth and potential distant dissemination. Cancer-induced angiogenesis is a result of increased expression of angiogenic factors, decreased expression of anti-angiogenic factors, or a combination of both. The assessment of angiogenesis has also emerged as a potentially useful biological prognostic and predictive factor in HNSCC. The aim of this review is to assess the level of current knowledge on the neo-angiogenesis markers involved in the biology, behavior, and prognosis of HNSCC. A search (between 1 January 2012 and 10 October 2022) was run in PubMed, Scopus, and Web of Science electronic databases. After full-text screening and application of inclusion/exclusion criteria, 84 articles are included. The current knowledge and debate on angiogenesis in HNSCC presented in the eligible articles are stratified as follows: (i) diagnostic markers; (ii) prognostic markers; (iii) predictive markers; and (iv) markers with a potential therapeutic role. Angiogenesis is a biological and pathological indicator of malignancies progression and has negative implications in prognosis of some solid tumors; several signals capable of tripping the “angiogenic switch” have also been identified in HNSCC. Although several studies suggested that antiangiogenic agents might be a valuable adjunct to conventional chemo-radiation of HNSCC, their long-term therapeutic value remains uncertain. Further investigations are required on combinations of antiangiogenic agents with conventional chemotherapeutic ones, immunotherapeutic and molecularly targeted agents in HNSCC. Additional data are necessary to pinpoint which patients could benefit most from these treatments.