This is a multicenter, open-label, dose-exploration and dose-expansion study to evaluate the safety, tolerability, antitumor activity, PK, pharmacodynamics, and immunogenicity of MEDI4736 in combination with tremelimumab in subjects with recurrent/metastatic squamous cell carcinoma of the head and neck.

Inclusion Criteria:

1. Male and female subjects
2. 18 years and older
3. Histologically or cytologically confirmed recurrent or metastatic squamous cell carcinoma of the head and neck (oral cavity, oropharynx, hypopharynx or larynx) that is incurable by local therapy.
4. Subjects who are treatment-naive or pretreated (prior anti-PD-1 or anti-PD-L1 required) in the recurrent/metastatic setting.
5. Subject eligibility will be based on PD-L1 expression as determined by a specified IHC assay.

Exclusion Criteria:

1. Any concurrent chemotherapy, immunotherapy, biologic, or hormonal therapy for cancer treatment, receipt of last dose of an approved anticancer therapy within 21 days
2. Concurrent or prior use of immunosuppressive medication within 14 days
3. Active or prior documented autoimmune or inflammatory disease within 3 years with some exceptions.