Stretchable displays have recently received increasing attention as input and/or output interfaces for the next-generation human-friendly electronic systems. A core component of the stretchable display is the stretchable electroluminescent (EL) devices, and they can be classified into two types, structurally stretchable EL devices and intrinsically stretchable EL devices, according to the mechanism for accomplishing the stretchability. We herein present recent advances in materials and design strategies for the stretchable EL devices. First, the stretchable devices based on ultrathin EL devices are introduced. The ultrathin EL devices are mechanically flexible like a thin paper, and they can become stretchable through various structural engineering, such as inducing a buckled structure, employing interconnects with stretchable geometries, and applying origami/kirigami techniques. Secondly, the intrinsically stretchable EL devices can be fabricated by using inherently stretchable electronic materials. For example, light-emitting electrochemical cells and EL devices with a simpler structure using alternating current, have been developed. Furthermore, novel stretchable semiconductor materials have been presented for the development of intrinsically stretchable light-emitting diodes. After discussing these two types of stretchable EL devices, we briefly discuss applications of deformable EL devices and conclude the review.