Intrinsically stretchable electroluminescent (is-EL) devices, whose components are made of mechanically soft and stretchable materials, are gaining significant attention as promising solutions for intrinsically stretchable displays. Compared to conventional stretchable devices with strain-distributing geometries, such as island-bridge or buckling structures, is-EL devices offer simpler device designs, enhanced mechanical reliability, and improved pixel density. This review highlights recent advancements in the development of is-EL devices, classifying them into two categories: alternating-current-driven electroluminescence devices (ACELs) and light-emitting diodes (LEDs). This work begins by exploring key materials for each component of is-EL devices, including electrodes, light-emitting layers, charge transport layers, and interconnections. This work also studies various device fabrication strategies for improving the luminous performance and pixel resolution. Then, this work discusses potential applications of is-EL devices, particularly focusing on wearable displays and multifunctional display technologies. Finally, this work concludes this review by commenting on the future outlook and unmet challenges.