Abstract: Maintaining the magnitude and intensity of human activities within the carrying capacity of resources and the environment is the core of the sustainable development theory. Therefore, how to assess the carrying capacity in a scientific way receives top priority among sustainability development strategies. The Planetary Boundaries Framework (PBF) that takes into account the Earth system as a whole provides new insights into assessing the carrying capacity of resources and the environment. The PBF has attracted considerable attentions and discussions within the sustainability science since its first appearance in the literature. However, the opportunities and challenges facing the PBF remain largely unexplored by the scientific community. This paper aims to fill in this gap by elaborating on the theoretical basis of the PBF and its conceptual evolution, revisiting the development and applications of the framework at the national, provincial, urban and organizational scales, identifying the challenges that the framework is facing and the solutions, and comparing the framework with the traditional paradigm for assessing the carrying capacity of resources and the environment. As a combination of historical experiences and scientific studies based on the theory of stable states and catastrophe in complex systems, the PBF serves as a useful supplement to the present assessments of carrying capacity. Primarily the downscaling of PBF to sub-global scales can be achieved through either top-down allocation or bottom-up integration. A systematic understanding of the linkages between these two pathways and their potential synergies would be of crucial significance to the development of the framework. However, we observe that there is a lack of clarity and transparency in the PBF regarding the scaling properties and interactions between various biophysical processes, leading to arguments over variables selection and boundaries setting. Besides, methodological challenges appear when we integrate PBF with tools for environmental impact assessment, such as environmental footprints and life cycle assessment, and extending the framework to socioeconomic dimensions. Therefore, there is a need for a deeper understanding of the PBF with respect to its theoretical basis, technical approaches and practical applications, so as to enhance the policy-guiding value of the framework as an approach to address the world's major public issues such as achieving Sustainable Development Goals (SDGs).

Key words: planetary boundaries, scale, biophysical process, threshold, carrying capacity