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Smart contract, one of the most successful applications of blockchain, is taking the world by storm, playing an essential role in the blockchain ecosystem. However, frequent smart contract security incidents not only result in tremendous economic losses but also destroy the blockchain-based credit system. The security and reliability of smart contracts thus gain extensive attention from researchers worldwide. In this survey, we first summarize the common types and typical cases of smart contract vulnerabilities from three levels, i.e., Solidity code layer, EVM execution layer, and Block dependency layer. Further, we review the research progress of smart contract vulnerability detection and classify existing counterparts into five categories, i.e., formal verification, symbolic execution, fuzzing detection, intermediate representation, and deep learning. Empirically, we take 300 real-world smart contracts deployed on Ethereum as the test samples and compare the representative methods in terms of accuracy, F1-Score, and average detection time. Finally, we discuss the challenges in the field of smart contract vulnerability detection and combine with the deep learning technology to look forward to future research directions.