Generative AI has rapidly advanced, enabling the creation of synthesized content like text, images, audio, and code. The high fidelity and authenticity of outputs from Deep Generative Models (DGMs) have raised significant copyright concerns. This paper explores copyright protection from a technical perspective, addressing issues related to source data owners, DGM users, and DGM providers. For data copyright, techniques such as unrecognizable examples, watermarks, machine unlearning, and dataset de-duplication are discussed. These methods aim to prevent unauthorized use of data and protect original works. For model copyright, strategies like watermarking and model theft prevention are considered. The paper also highlights the limitations of current techniques and identifies areas for future research. It discusses various computational methods for copyright protection in image, text, and other domains, emphasizing the need for sustainable and ethical development of generative AI. Key techniques include adversarial examples, diffusion models, and watermarking strategies to ensure data and model copyright protection. The paper provides an overview of existing methods and their applications in different scenarios, aiming to address the complex legal and ethical challenges associated with generative AI.Generative AI has rapidly advanced, enabling the creation of synthesized content like text, images, audio, and code. The high fidelity and authenticity of outputs from Deep Generative Models (DGMs) have raised significant copyright concerns. This paper explores copyright protection from a technical perspective, addressing issues related to source data owners, DGM users, and DGM providers. For data copyright, techniques such as unrecognizable examples, watermarks, machine unlearning, and dataset de-duplication are discussed. These methods aim to prevent unauthorized use of data and protect original works. For model copyright, strategies like watermarking and model theft prevention are considered. The paper also highlights the limitations of current techniques and identifies areas for future research. It discusses various computational methods for copyright protection in image, text, and other domains, emphasizing the need for sustainable and ethical development of generative AI. Key techniques include adversarial examples, diffusion models, and watermarking strategies to ensure data and model copyright protection. The paper provides an overview of existing methods and their applications in different scenarios, aiming to address the complex legal and ethical challenges associated with generative AI.