Today's blockchains suffer from low throughput and high latency, which impedes their widespread adoption of more complex applications like smart contracts. In this article, we propose a novel paradigm for smart contract execution. It distinguishes between consensus nodes and execution nodes: different groups of execution nodes can execute transactions in parallel; meanwhile, consensus nodes can asynchronously order transactions and process execution results. Moreover, it requires no coordination among execution nodes and can effectively prevent livelocks. We show two ways of applying this paradigm to blockchains. First, we show how we can make Ethereum support parallel and asynchronous contract execution without hard-forks . Then, we propose a new public, permissionless blockchain. Our benchmark shows that, with a fast consensus layer, it can provide a high throughput even for complex transactions like Cryptokitties gene mixing. It can also protect simple transactions from being starved by complex transactions.