Blockchains such as Ethereum serially execute smart contract transactions in a block, which can strictly guarantee the consistency of the blockchain state between nodes after execution, but it has become a serious bottleneck restricting the throughput of these blockchains. Therefore, the use of parallel methods to optimize the execution of smart contract transactions has gradually become the focus of industry and academia. This study summarizes the research progresses of the parallel execution methods of smart contracts in blockchains, and proposes a research framework. From the perspective of the phases of parallel execution of smart contracts, the framework condenses four parallel execution models of smart contracts, namely the parallel execution model based on static analysis, the parallel execution model based on dynamic analysis, the parallel execution model between nodes and the divide-and-conquer parallel execution model, and describes the typical parallel execution methods under each model. Finally, this study discusses the factors affecting parallel execution such as the transaction dependency graph and concurrency control strategies, and proposes future research directions.