Antennas are provided for electronic devices such as portable computers. An electronic device may have a housing in which an antenna is mounted. The housing may have an antenna window for the antenna. The antenna window may be formed from dielectric or from antenna window slots in a conductive member such as a conductive wall of the electronic device housing. An antenna may have an antenna resonating element that is backed by a conductive antenna cavity. The antenna resonating element may have antenna resonating element slots or may be formed using other antenna configurations such as inverted-F configurations. The antenna cavity may have conductive vertical sidewalls and a conductive rear wall. The antenna cavity walls may be formed from conductive layers on a dielectric antenna support structure.