Intriguing rich phase transitions and multiferroic behavior in (110)-oriented BiFeO3 epitaxial films are studied by first-principles calculations. We demonstrate that a BiFeO3 (110)(c) film undergoes complicated monoclinic-monoclinic-orthorhombic (M-a-M-b-O) phase transitions depending on the epitaxial strain conditions. During the phase transition, ferroelectric spontaneous polarization and a magnetic moment due to weak ferromagnetism rotate in different ways, leading to different anisotropies in the magnetoelectric response of the BiFeO3 (110)(c) film. Electronic structure analysis reveals that applying compression worsens the resistance to current leakage of the BiFeO3 film. (C) 2012 Elsevier B.V. All rights reserved.