An electronic device may be provided with a display. The display may be mounted in a display housing having multiple display housing layers. The display housing layers may include metal layers and fiber composite layers. A fiber composite display housing layer may have an array of dimples. The fiber composite display housing layer may be attached to a planar metal layer using adhesive. An array of openings may be formed in the metal layer to lighten the display housing. A foam layer or other core may be sandwiched between display housing layers. Components may be embedded in the foam. Edge members may run along peripheral edges of the display housing layers. Electrical components may be mounted on printed circuits and housed within cavities in the display housing. The electrical components may include light-emitting diodes for a display. Heat from the electrical components may be dissipated in the metal layer.