Blockchain technology is facing critical issues of scalability, efficiency and sustainability. These problems are necessary to solve if blockchain is to become a technology that can be used responsibly. Useful quantum computers could potentially be developed by the time that blockchain will be widely implemented for mission-critical work at financial and other institutions. Quantum computing will not only cause challenges for blockchain, but can also be harnessed to better implement parts of blockchain technologies including cryptocurrencies. We review the work that has been done in the area of quantum blockchain and hybrid quantum–classical blockchain technology and discuss open questions that remain.