The Atomic and Molecular Data Unit organized the Joint ICTP-IAEA Conference on Models and Data for Plasma-Material Interaction in Fusion Devices at ICTP in Trieste, Italy, 3-7 November 2014. The meeting brought together researchers from fusion energy science and materials science in order to review advances in computational studies of plasma-material interaction (PMI) processes and evolution of material microstructure in fusion devices, including effects of radiation damage and with special interest in hydrogen (tritium) trapping and transport in wall material. The proceedings of the meeting are summarized in this report.