In recent decades, the concept of sustainability has taken on a key role in the agendas of political decision-makers, businesses, and society. Brands have incorporated attributes associated with the concept of sustainability, making it essential to understand how these attributes are perceived and how they influence purchasing decisions. Young consumers tend to be well informed about social and environmental aspects and are more sensitive than previous generations to environmental issues. Although Gen Z’s purchasing intentions are influenced by the sustainable practices of organizations, their preferences are not fully understood. Recent studies have shown that the sustainability component associated with the brand influences Gen Z’s purchase intentions, and that social and economic aspects are at the root of this, emphasizing the importance of corporate social responsibility and transparent brand communication in terms of sustainability. Understanding how the sustainability component of brands influences the purchasing decisions of young consumers is fundamental for defining future branding strategies. The aim of this paper is to describe the state of the art of the relationship between the sustainability component of the brand and the purchase intention of Gen Z, based on the literature. The topic has not yet been widely studied, so it leaves clues for future development.