This is a phase I, open-label, dose-escalation study of CUDC-101 in patients with advanced and refractory solid tumors. CUDC-101 is a multi-targeted agent designed to inhibit epidermal growth factor receptor (EGFR), human epidermal growth factor receptor Type 2(Her2) and histone deacetylase (HDAC). The study is designed to establish the safety, including the maximum tolerated dose, the pharmacokinetics, and the anti-tumor activity of CUDC-101.