Distributed and decentralized applications, e.g., Decentralized Finance (DeFi), require high performance in terms of throughput and latency, e.g., while the Visa payment service is able to handle tens of thousands of transactions per second, naive implementations of permissioned blockchains handle only hundreds of transactions per second. In general, “order” and “execution” are the two main stages of processing transactions in permissioned blockchains. The order stage uses a consensus protocol to assign an order to each transaction in the global service history, while the execution stage executes the transaction in the specified order. Permissioned blockchains need to parallelize the processing of different transactions in the order or execution phase to improve the system’s overall performance. In this chapter, we focus on the execution stage and briefly discuss different permissioned blockchain system’s paradigms such as order-execute (OX), execute-order-validate (XOV), and order-parallel execute (OXII). We then discuss the OXII paradigm in detail and show how this paradigm has been used in ParBlockchain to improve the performance of permissioned blockchains.