Climate change and global warming are the biggest challenges of the current generation. Every industry has contributed to the climate change and global warming. Even the apparel industry cannot avoid the criticism regarding fast fashion and its contribution to the pollution. The transition to the decarbonized economy is in progress. All aspects of business functions are influenced by climate change. Sustainable development and climate change are closely linked, and business plays the key role in addressing and finding solutions to the challenges of climate change. Luxury brands are the trendsetters and tastemakers. They are the leaders in the fashion industry and therefore responsible for improving on sustainability as well. Even luxury business cannot avoid environmental issues. The relation between luxury and sustainability is explored with the Burberry case based on the Triple Bottom Line (TBL) framework. There are various ways for luxury brands to excel in sustainability and affect other companies’ practices. The companies can incorporate the concept of sustainability in their brand stories as part of the branding process. They can also improve demand planning accuracy and produce upcycled goods. Centering on Burberry’s case, this paper aims to explore the current sustainable practices of luxury business along with its future direction toward sustainable development. Its contribution and directions for both researchers and business practitioners are discussed.