Blockchain is the basis of the Internet of value. However, data and value silos arise from independent blockchain systems. Blockchain interoperability (also known as cross-chain operability) is essential for breaking inter-chain barriers and building a blockchain network. After differentiating between the blockchain interoperability in the narrow sense and that in the broad sense, this study redefines the former concept and abstracts out two primary operations: cross-chain reading and cross-chain writing. Subsequently, it summarizes three key technical problems that need to be resolved for achieving the blockchain interoperability in the narrow sense: cross-chain information transmission, cross-chain trust transfer, and cross-chain operation atomicity guarantee. Then, the study reviews the current research status of the three problems systematically and makes comparisons from multiple perspectives. Furthermore, it analyzes some representative holistic solutions from the perspective of the key technical problems. Finally, several research directions deserving of further exploration are also presented.