Driven by recent advancements in machine learning, mobile edge computing (MEC) and the Internet of things (IoT), artificial intelligence (AI) has become an emerging technology. Traditional machine learning approaches require the training data to be collected and processed in centralized servers. With the advent of new decentralized machine learning approaches and mobile edge computing, the IoT on-device data training has now become possible. To realize AI at the edge of the network, IoT devices can offload training tasks to MEC servers. However, those distributed frameworks of edge intelligence also introduce some new challenges, such as user privacy and data security. To handle these problems, blockchain has been considered as a promising solution. As a distributed smart ledger, blockchain is renowned for high scalability, privacy-preserving, and decentralization. This technology is also featured with automated script execution and immutable data records in a trusted manner. In recent years, as quantum computers become more and more promising, blockchain is also facing potential threats from quantum algorithms. In this chapter, we provide an overview of the current state-of-the-art in these cutting-edge technologies by summarizing the available literature in the research field of blockchain-based MEC, machine learning, secure data sharing, and basic introduction of post-quantum blockchain. We also discuss the real-world use cases and outline the challenges of blockchain-empowered intelligence.