The sixth generation (6G) of wireless communications is envisioned as a transformative platform that will seamlessly integrate communication, sensing, computing, and intelligence to support immersive, autonomous, and human-centric services. Through capabilities such as terabit-per-second connectivity, pervasive artificial intelligence, integrated sensing and communication, and global coverage across terrestrial and non-terrestrial infrastructures, 6G is expected to become a cornerstone of future digital societies. However, realizing this ambitious vision poses a fundamental challenge: sustainability. The rapid growth of network traffic, edge intelligence, cloud computing, and connected devices threatens to significantly increase the energy consumption and carbon footprint of communication systems if sustainability is not embedded into their design from the outset.