Main objectives of this study are to 1) evaluate the time to progression (primary endpoint) with the combination of pemetrexed and bevacizumab in recurrent or metastatic head and neck cancer; 2) evaluate the objective response rate, duration of response, overall survival, and toxicities associated with the above therapy and 3) collect tumor tissue from previous diagnostic procedures and blood specimens prospectively, before and after therapy, for future correlative studies.