The 5-year overall survival rate remains approximately 50% for head and neck (H&N) cancer patients, even though new cancer drugs have been approved for clinical use since 2016. Cancer drug studies are now moving toward the use of three-dimensional culture models for better emulating the unique tumor microenvironment (TME) and better predicting in vivo response to cancer treatments. Distinctive TME features, such as tumor geometry, heterogenous cellularity, and hypoxic cues, notably affect tissue aggressiveness and drug resistance. However, these features have not been fully incorporated into in vitro H&N cancer models. This review paper aims to provide a scholarly assessment of the designs, contributions, and limitations of in vitro models in H&N cancer drug research. We first review the TME features of H&N cancer that are most relevant to in vitro drug evaluation. We then evaluate a selection of advanced culture models, namely, spheroids, organotypic models, and microfluidic chips, in their applications for H&N cancer drug research. Lastly, we propose future opportunities of in vitro H&N cancer research in the prospects of high-throughput drug screening and patient-specific drug evaluation.