Organic light-emitting diodes (OLEDs) are remarkably promising display devices that can function in mechanically flexible configurations on a plastic substrate due to various compelling properties including organic constituents, ultrathin and simple structure, and low-temperature fabrication. In spite of successful demonstrations of flexible OLEDs, some technical issues of containing relatively thick transparent electrodes made of ceramic materials and an unstable flexible encapsulation system have impeded reaching high levels of reliability and durability toward full commercialization. This review covers recent developments in structure designs for highly durable flexible OLEDs, ranging from alternative transparent electrodes to thin-film encapsulation layers, in which solution concepts for the existing critical issues of flexible OLEDs are addressed. Emerging unusual substrates and their application strategies are additionally introduced to find intimations of future display technologies and hence to disclose non-classic flexible OLEDs.