As the demand for flexible, rollable, and foldable displays grows, various state-of-the-art component technologies, including thin-film transistors (TFTs), electrodes, thin-film encapsulations (TFEs), and touch screen panels, have been developed based on organic light-emitting diodes (OLEDs) with flexible organic layers. Developing highly reliable flexible OLEDs is essential to realize flexible displays, but the flexible encapsulation technology still has technical difficulties and issues to be addressed. This review covers the recent developments in encapsulation technologies, particularly their material and structural designs, for highly reliable, flexible OLEDs. The solution concepts for the existing technical hurdles in flexible encapsulations are addressed. Among the various advanced flexible encapsulation technologies developed so far, neutral-axis engineering with a thin metal layer and a crack arrester is introduced.