This thesis focuses on the use of metamaterials in mobile phone devices in order to improve antenna performances, e.g. to investigate if they can reduce the peak of SAR in the human head. The purpose is to present metamaterials in a general way as many researches do t provide general background and kwledge, and focus on very specific uses and topics. As many researches focus on the use of metamaterials with antennas, the second objective is to analyze if they could possibly improve the performances of antennas. Thanks to FDTD simulations, several configurations have been investigated. The effective reduction of the fields thanks to metamaterials is investigated because improving user's safety compliance and handset performances is a major interest of mobile phone designers.