This paper explores the design of low-carbon neural network algorithms and their applications in industry and large-scale models, introducing the concept of low-carbon algorithms and the perspective of carbon footprints in deep learning. The paper then discusses various design strategies such as pruning, quantization, and low-rank decomposition, which significantly reduce resource consumption in data centers and network devices, promoting green computing. It also highlights practical applications, including low-precision computation, efficient hardware design, and hardware acceleration, demonstrating their potential to reduce energy waste and environmental impact. For large language models(LLMs), the paper covers compression techniques and model structure optimization to mitigate the environmental burden of these high-resource-demand models. Additionally, it proposes evaluation criteria to measure the efficiency of different algorithms and looks ahead to the future development of low-carbon algorithms and their significance for sustainable development. This work aims to advance the research and application of low-carbon algorithms, contributing to the creation of a sustainable digital society.