Given the ongoing transition towards a more decentralised and adaptive energy system, the potential of blockchain-enabled smart contracts for the energy sector is being increasingly recognised. Due to their self-executing, customisable and tamper-proof nature, they are seen as a key technology for enabling the transition to a more efficient, transparent and transactive energy market. The applications of smart contracts include coordination of smart electric vehicle charging, automated demand-side response, peer-to-peer energy trading and allocation of the control duties amongst the network operators. Nevertheless, their use in the energy sector is still in its early stages as there are many open challenges related to security, privacy, scalability and billing. In this paper, we systematically review 178 peer-reviewed publications and 13 innovation projects, providing a thorough analysis of the strengths and weaknesses of smart contracts used in the energy sector. This work offers a broad perspective on the opportunities and challenges that stakeholders using this technology face, in both current and emergent markets, such as peer-to-peer energy trading platforms. To provide a roadmap for researchers and practitioners interested in the technology, we propose a systematic model of the smart contracting process, by developing a novel 6-layer architecture, as well as presenting a sample energy contract in pseudocode form and as open-source code. Our analysis focuses on the two mainstream application areas we identify for smart contract use in this area: energy and flexibility trading, and distributed control. The paper concludes with a comprehensive, critical discussion of the advantages and challenges that must be addressed in the area of smart contracts and blockchains in energy, and a set of recommendations that researchers and developers should consider when applying smart contracts to energy system settings.