An electronic device may be provided with an organic light-emitting diode display with minimized border regions. The border regions may be minimized by providing conductive structures (microvia 73) that pass through polymer layers (48, 52) of the display and/or conductive structures that wrap around an edge of the display and couple conductive traces (51) on the display to conductive traces (59) on additional circuitry (flexible printed circuit 62) that is mounted behind the display.
