Generative AI has witnessed rapid advancement in recent years, expanding their capabilities to create synthesized content such as text, images, audio, and code. The high fidelity and authenticity of contents generated by these Deep Generative Models (DGMs) have sparked significant copyright concerns. There have been various legal debates on how to effectively safeguard copyrights in DGMs. This work delves into this issue by providing a comprehensive overview of copyright protection from a technical perspective. We examine from two distinct viewpoints: the copyrights pertaining to the source data held by the data owners and those of the generative models maintained by the model builders. For data copyright, we delve into methods data owners can protect their content and DGMs can be utilized without infringing upon these rights. For model copyright, our discussion extends to strategies for preventing model theft and identifying outputs generated by specific models. Finally, we highlight the limitations of existing techniques and identify areas that remain unexplored. Furthermore, we discuss prospective directions for the future of copyright protection, underscoring its importance for the sustainable and ethical development of Generative AI.

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