• Histologically or cytologically confirmed recurrent and/or metastatic squamous cell carcinoma of the head and neck (R/M HNSCC), which is considered incurable by local therapies.

• Primary tumor locations: oropharynx, oral cavity, hypopharynx, larynx, nasopharynx, and sinonasal. Unknown primary is also eligible.

• Age: Participants must be at least 18 years old.

• ECOG Performance Status: Must be 0-1.

• Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria.

• For oropharyngeal cancer: HPV (p16) testing is required. p16 Immunohistochemistry (IHC) is sufficient for Human Papillomavirus (HPV) testing.

• Programmed cell death ligand 1 (PD-L1) combined positive score (CPS) : For patients with previously untreated R/M disease, a combined positive score (CPS) of 1 or greater is required. There is no PD-L1 restriction for patients who have previously received anti-PD(L)1 therapy.

• Recovery to baseline or ≤ Grade 1 severity (CTCAE v5) from any adverse events (AEs), including immune-related AEs from prior treatments.

• Adequate organ and marrow function, including:

• Absolute neutrophil count (ANC) ≥ 1500/mm3.

• Platelets ≥ 100,000/mm3.

• Hemoglobin ≥ 9 g/dL.

• Normal liver and kidney function.

• Capable of understanding and complying with the protocol requirements and must have signed the informed consent document.

• Contraception: Sexually active fertile subjects must agree to use a highly effective method of contraception during the study and for 2 months after the last dose of cetuximab and 4 months after the last dose of pembrolizumab.