Blockchain technology is used in Internet of Things （IoT） due to its characteristics of decentralization and encryption. However， the traditional blockchain has problems such as poor scalability， high latency， high consumption of cryptographic components， complex consensus computing and large data storage scale in IoT environment. In view of the poor performance of traditional blockchain in IoT devices， the lightweight technology of blockchain was reviewed. Firstly， the blockchain architectures were divided into single-chain structure and Directed Acyclic Graph （DAG） structure， and the lightweight operations in the two types of blockchain architectures were compared. Secondly， the lightweight hash function was analyzed from the perspectives of iterative structure， compression function and hardware implementation. Thirdly， the consensus algorithms and the lightweight schemes in storage were introduced. Finally， the design ideas of blockchain lightweight technology were summarized based on the literature research results， and the future research directions were prospected.

Most of the current consensus algorithms require high computing power or specific communication environment and are not suitable for resource-constrained Internet of Things （IoT）. In view of the limitations of the traditional consensus algorithms in blockchain applied to IoT， blockchain consensus algorithms for IoT were reviewed. Firstly， the consensus algorithms for IoT were introduced and summarized from three categories： improved consensus algorithms based on Practical Byzantine Fault Tolerance （PBFT）， improved algorithms based on other consensus algorithms， and new blockchain consensus algorithms suitable for IoT. Secondly， a basic evaluation index system of consensus algorithms was established to compare consensus algorithms from five aspects： decentralization， scalability， security， latency， and energy consumption. Finally， the challenges and future research directions of consensus algorithms for IoT were analyzed. Analysis of the basic evaluation index system shows that the new blockchain consensus algorithms are more suitable for IoT than the improved consensus algorithms based on the traditional consensus algorithms， providing a reference for research on blockchain consensus algorithms for IoT.