This is an open-label, phase I study of cetuximab and differing dose levels of dasatinib in adult patients with advanced solid malignancies. Cetuximab will be administered as an intravenous infusion on a standard dose and schedule (weekly, with the first dose at 400 mg/m2 and all subsequent weekly doses at 250 mg/m2). Dasatinib will be administered orally on a continuous schedule at the following dose levels: 100 mg QD (once a day), 150 mg QD, and 200 mg QD. Three to six patients will be enrolled at each dose level, and the final recommended phase II cohort will be expanded to include up to 12 additional patients. The doses will be escalated in successive cohorts of patients. On cycle 1, dasatinib administration will start one day prior to cetuximab administration. One cycle will be defined as 21 days, and cycles will continue until progression of disease or intolerable toxicities occur. Peripheral blood samples and pharmacokinetic blood samples will be taken on days 0, 1, 15, and 16 of Cycle 1 only. In patients with accessible tumor that give consent, patients will undergo a baseline tumor biopsy and a repeat biopsy after 14-21 days of the first cycle.