Buffer-aided cooperative networks (BACNs) have garnered significant attention due to their potential applications in beyond fifth generation (B5G) or sixth generation (6G) critical scenarios. This article explores various typical application scenarios of buffer-aided relaying in B5G/6G networks to emphasize the importance of incorporating BACN. Additionally, we delve into the crucial technical challenges in BACN, including stringent delay constraints, high reliability, imperfect channel state information (CSI), transmission security, and integrated network architecture. To address the challenges, we propose leveraging deep learning-based methods for the design and operation of B5G/6G networks with BACN, deviating from conventional buffer-aided relay selection approaches. In particular, we present two case studies to demonstrate the efficacy of centralized deep reinforcement learning (DRL) and decentralized DRL in buffer-aided non-terrestrial networks. Finally, we outline future research directions in B5G/6G that pertain to the utilization of BACN.