Electronic devices may include displays having backlight structures that include optical films. The optical films may help guide light from the backlight structures to display layers that generate display images using the light. The optical films may be attached together at one or more locations. The optical films may be attached to a structural member of the backlight structures. The structural member may be formed along each edge of the optical films and prevent the optical films from sliding within the display. Each optical film may be designed to expand to a common lateral size when the display is operated at a display operating temperature. The optical films may each include an elongated opening such as a slot through which a pin can be placed to partially constrain the movement of the optical films while allowing the optical films to expand or contract under changing thermal conditions in the display.