An electronic device may be provided with electrical components mounted in a housing. The electronic device may include wireless transceiver circuitry and antenna structures. A display may be mounted in the housing. The display may have a transparent layer such as display cover layer. The display cover layer may have an inner surface with a recess. The recess may be a groove that runs along a peripheral edge of the display cover layer. An antenna structure such as an inverted-F antenna resonating element may be formed from a metal trace on a plastic support structure. The metal trace and support structure may be mounted in the groove with adhesive. The housing may be a metal housing that forms an antenna ground. Springs may be used in forming an antenna feed and an antenna return path that couples the antenna resonating element to ground.