As the next-generation Internet characterized by readability, writability, and ownability, Web 3.0 necessitates the fusion of blockchain and artificial intelligence (AI) technologies to realize its vision of decentralization, user autonomy, and intelligent openness. To this end, this article proposes the integration of “AI for blockchain” and “blockchain for AI” to form a bidirectional enhancement loop, for establishing genuinely intelligent blockchains and ushering in a new paradigm referred to as blockchain intelligence. On this basis, the technical architecture of intelligent blockchains is proposed, which infuses intelligence into every layer of traditional blockchain architectures while enables the parallel execution between virtual and artificial intelligent blockchain systems. This architecture facilitates blockchain systems to cultivate an ecosystem of intelligence, extending from foundation intelligence to application intelligence. Moreover, the core attributes of blockchain intelligence are examined, from the perspectives of smart contracts, data, identity, and governance. Furthermore, the main challenges and research issues faced by blockchain intelligence are outlined. This article is committed to the advancement of blockchain intelligence, laying the groundwork for Web 3.0 and the impending era of smart societies.