An electronic device may be provided with a display having substrate layers such as a color filter layer, thin-film transistor layer, or other display layers. An array of pixels may be formed from thin-film circuitry on a display layer. A color filter layer may be formed from an array of color filter elements on a display layer. The color filter elements may provide the array of pixels with the ability to display color images. In a liquid crystal display configuration, a liquid crystal layer may be interposed between the substrate layers. A ring of sealant may surround the liquid crystal layer and may be interposed between the substrate layers. The display may have a periphery. The substrate layers may be welded with a glass weld such as a laser glass weld or other weld on an edge surface of the substrate layers running along the periphery.