<p>As global warming intensifies, extreme weather events are becoming increasingly frequent. Humanity is compelled to confront unprecedented challenges. There is a growing public clamor for transitioning to low-carbon living and sustainable production. This comprehensive survey focuses on traditional machine learning, advanced deep learning and latest federated learning methods for carbon emission, carbon footprint and carbon pricing prediction tasks. Firstly, a systematic overview of carbon emission prediction and management with some traditional machine learning methods are provided, including carbon emission prediction model, carbon market and carbon price prediction and industrial and energy optimization. Then, we conduct a comprehensive summary of some advanced deep learning methods for above tasks. In recent years, federated learning, as a distributed learning mode with security and privacy protection, has been widely used in some sensitive domains of data security. Hence, we further discuss about federated learning pattern for carbon emission, including green federated learning, carbon-efficient federated learning, energy-efficient federated learning methods. Finally, we propose some potential research problems as future directions from various aspects, including model interpretability, robustness and generalization across different regions and sectors, real-time prediction and adaptive learning systems, multi-source heterogeneous data fusion and optimization, data security and privacy protection.</p>