An electronic device may have hybrid antennas that include slot antenna resonating elements formed from slots in a ground plane and planar inverted-F antenna resonating elements. The planar inverted-F antenna resonating elements may each have a planar metal member that overlaps one of the slots. The slot of each slot antenna resonating element may divide the ground plane into first and second portions. A return path and feed may be coupled in parallel between the planar metal member and the first portion of the ground plane. Tunable components such as tunable inductors may be used to tune the hybrid antennas. A tunable inductor may bridge the slot in hybrid antenna, may be coupled between the planar metal member of the planar inverted-F antenna resonating element and the ground plane, or multiple tunable inductors may bridge the slot on opposing sides of the planar inverted-F antenna resonating element.