As device form factors evolve towards increased complexity and flexibility, the role of adhesives within the display module stack becomes increasingly crucial. These adhesives are essential for bonding functional layers with minimal thickness while mitigating stress during the dynamic behavior of flexible devices. This paper offers a comprehensive overview of the essential properties of adhesives - such as adhesion, viscoelasticity, optical characteristics, and environmental reliability - necessary for the stable operation of flexible display devices across diverse form factors and environments. In particular, it provides an in-depth look at ongoing research in simulation, material selection, polymer network control, and the integration of new functionalities to achieve optimal performance. Furthermore, this paper discusses extensive research outcomes addressing the growing demand for sustainable solutions. Building on this knowledge, we highlight the future direction of adhesives for flexible displays.