Blockchain technology has experienced a rapid growth in recent years, leading to the emergence of various blockchain-based applications. One of the most prominent examples of such applications is the creation of asset in the form of token. However, asset on a chain are difficult to transfer to another chain due to the heterogeneity of different types of blockchains. Cross-chain asset transfer technology enables the transfer of value between blockchains and can improve the scalability of blockchains. This paper provides a systematic overview of cross-chain asset transfer schemes, introducing their classification, main challenges, and representative implementations. Furthermore, this paper summarizes and proposes the future research directions of cross-chain asset transfer schemes.