Despite the current progress in the development of new concepts of precision medicine for head and neck squamous cell carcinoma (HNSCC), in particular targeted therapies and immune checkpoint inhibition (CPI), overall survival rates have not improved during the last decades. This is, on the one hand, caused by the fact that a significant number of patients presents with late stage disease at the time of diagnosis, on the other hand HNSCC frequently develop therapeutic resistance. Distinct intratumoral and intertumoral heterogeneity is one of the strongest features in HNSCC and has hindered both the identification of specific biomarkers and the establishment of targeted therapies for this disease so far. To date, there is a paucity of reliable preclinical models, particularly those that can predict responses to immune CPI, as these models require an intact tumor microenvironment (TME). The “ideal” preclinical cancer model is supposed to take both the TME as well as tumor heterogeneity into account. Although HNSCC patients are frequently studied in clinical trials, there is a lack of reliable prognostic biomarkers allowing a better stratification of individuals who might benefit from new concepts of targeted or immunotherapeutic strategies. Emerging evidence indicates that cancer stem cells (CSCs) are highly tumorigenic. Through the process of stemness, epithelial cells acquire an invasive phenotype contributing to metastasis and recurrence. Specific markers for CSC such as CD133 and CD44 expression and ALDH activity help to identify CSC in HNSCC. For the majority of patients, allocation of treatment regimens is simply based on histological diagnosis and on tumor location and disease staging (clinical risk assessments) rather than on specific or individual tumor biology. Hence there is an urgent need for tools to stratify HNSCC patients and pave the way for personalized therapeutic options. This work reviews the current literature on novel approaches in implementing three-dimensional (3D) HNSCC in vitro and in vivo tumor models in the clinical daily routine. Stem-cell based assays will be particularly discussed. Those models are highly anticipated to serve as a preclinical prediction platform for the evaluation of stable biomarkers and for therapeutic efficacy testing.