Head and neck squamous cell carcinoma (HNSCC) is a common malignancy that develops in or around the throat, larynx, nose, sinuses and mouth, and is mostly treated with a combination of chemo- and radiotherapy (RT). The main goal of RT is to kill enough of the cancer cell population, whilst preserving the surrounding normal and healthy tissue. The mechanisms by which conventional photon RT achieves this have been extensively studied over several decades, but little is known about the cell death pathways that are activated in response to RT of increasing linear energy transfer (LET), including proton beam therapy and heavy ions. Here, we provide an up-to-date review on the observed radiobiological effects of low- versus high-LET RT in HNSCC cell models, particularly in the context of specific cell death mechanisms, including apoptosis, necrosis, autophagy, senescence and mitotic death. We also detail some of the current therapeutic strategies targeting cell death pathways that have been investigated to enhance the radiosensitivity of HNSCC cells in response to RT, including those that may present with clinical opportunities for eventual patient benefit.