An electronic device may include display layers such as liquid crystal display layers and a backlight unit that provides illumination for the display layers. The backlight unit may include light-emitting diodes that emit light into the edge of a light guide film. To minimize the inactive area of the display, the light-emitting diodes may be tightly spaced to approximate a line light source instead of point light sources. Color and/or luminance compensation layers may be incorporated at various locations within the backlight structures to ensure that the backlight provided to the display layers is homogenous. A thin-film transistor layer of the display may be coupled to a printed circuit board by a flexible printed circuit. The flexible printed circuit may have additional solder mask layers to improve robustness, may include encapsulation, and may have traces with a varying pitch.