In order to ensure the network-wide consensus and tamper proof of the transaction ledger, the miner nodes are required to possess strong computing and storage resource in the traditional blockchain technology. It greatly limits the resource-constrained devices to join in the blockchain systems. In recent years, blockchain technology has been expanded in many fields, such as financial economy, health care, Internet of Things, supply chain, etc.. However, there are a large number of devices with weak computing power and low storage capacity in these application scenarios, which brings great challenges to the application of blockchain. Therefore, lightweight blockchain technology is emerging. In this paper, we summarize some related works of lightweight blockchain from the two aspects of lightweight computing and storage. We compare and analyze their advantages and disadvantages. Finally, we look forward to the future development of the lightweight blockchain systems.