The global challenges of sustainability intensify the demand for advanced decision-making systems capable of integrating cognitive capabilities. This survey article comprehensively examines the recent advancements, diverse applications, state-of-the-art techniques, and persistent challenges in cognition and context-aware decision-making systems (CCA-DMS) aimed at fostering sustainability across smart environments. We first present the cognition and context-aware decision-making applications covering topics such as environmental conservation, energy management, urban planning, resource usage, and healthcare. Subsequently, we make a categorization of techniques, methods and cognition-aware models employed. Through a systematic review of the literature, we highlight the significant contributions and breakthroughs in each use case. Furthermore, we identify and analyze the open challenges and research gaps that remain to be addressed, including data gathering, scalability, interpretability, robustness, and ethical considerations. By synthesizing the current state-of-the-art and future directions, this survey serves as a valuable resource for researchers, practitioners, and policymakers interested in harnessing CCA-DMS to address the complex sustainability challenges facing our planet.