Blockchain is a technology that combines distributed consensus, encryption, timestamps, etc., to achieve peer-to-peer trading, coordination, and collaboration without relying on any third-party centralization organization. In recent years, the rapid development of blockchain technology has aroused great interest from industry and academia. However, the problem of storage scalability of blockchain has increased the threshold of blockchain devices and has become a bottleneck for blockchain applications. This paper introduces the basic principle and storage model of blockchain, and analyzes the storage problems faced by current blockchain. Then, for the problem of blockchain storage scalability, from two perspectives of off-chain storage and on-chain storage, the principles and ideas of the existing solutions are discussed. Finally, based on the research progress of the storage scalability of blockchain and the problems of these solutions, directions are provided for future research work.