An electronic device may have a housing with portions that slide relative to each other. A display may be supported on a surface of the housing such as on a front face of the housing. The housing portions may slide between an unexpanded state in which the display has an unexpanded viewable area on the front face and an expanded state in which the display has an expanded viewable area on the front face that is greater than the unexpanded viewable area. The housing portions may have interior regions that contain electrical components. The display may be formed from a flexible display substrate. A portion of a flexible display may be stored in an interior region of the housing when the housing is in the unexpanded state. In the unexpanded state, the flexible display may have one or more bends and may double back on itself one or more times.