One potential use for various types of electronics is to integrate them into fabrics, for clothing, tents or advertising displays. This has been achieved for various devices by combining hard electronics with a soft rubbery matrix, and connecting them together with long wiggley wires that straighten rather than stretch. But these have issues with the complexity of their manufacture, and you obviously can't manufacture a panel which glows evenly all over it without adding more complexity.
Zhibin Yu and collegues at the University of California Los Angeles, have taken a different tack. They have manufactured electrodes out of a flexible polymer with conducting carbon nanotubes suspended in it. Enough of the nanotubes touch each other to transfer a current throughout the device. Nanotubes are particularly useful as they are very good at injecting electrons into or extracting them from plastic semiconductors. This means that if a large flat stretchable plastic light emmitting diode structure is sandwiched between two layers of the transparent electrodes, you get a light emmitting diode. Which continues glowing when you stretch the device by about 45%.
This device is very experimental, not least as the plastic has to be heated above 56°C to behave as a rubber rather than a hard plastic. Though this could still be useful for custom shaping displays after they have been made, true stretchable displays will wait for some more development.