Smart contracts are regarded as one of the most promising and appealing notions in blockchain technology. Their self-enforcing and event-driven features make some online activities possible without a trusted third party. Nevertheless, problems such as miscellaneous attacks, privacy leakage, and low processing rates pre-vent them from being widely applied. Various schemes and tools have been proposed to facilitate the construction and execution of secure smart contracts. However, a comprehensive survey for these proposals is absent, hindering new researchers and developers from a quick start. This paper surveys the literature and online resources on smart contract construction and execution over the period 2008-2020. We divide the studies into three categories: (1) design paradigms that give examples and patterns on contract construction, (2) design tools that facilitate the development of secure smart contracts, and (3) extensions and alternatives that improve the privacy or efficiency of the system. We start by grouping the relevant construction schemes into the first two categories. We then review the execution mechanisms in the last category and further divide the state-of-the-art solutions into three classes: private contracts with extra tools, off-chain channels, and extensions on core functionalities. Finally, we summarize several challenges and identify future research directions toward developing secure, privacy-preserving, and efficient smart contracts.