Recent years have witnessed remarkable developments and increasingly deepened integrations between blockchain as a decentralized computing architecture and auction as an efficient resource allocation approach. Typically, blockchain can help provide a secured and trusted distributed environment for various auction scenarios, while auction is particularly suitable for designing resource allocation and pricing mechanisms in blockchain systems. As such, integrative research on blockchain and auction developed rapidly and attracted widespread attention in various fields ranging from academia to financial, industrial, and social services. However, a comprehensive survey on this interdisciplinary topic is still nonexistent, which motivates our work. In this article, we aim to fill this important research gap by reviewing the related literature. We first conducted a brief overview of blockchain technology and auction theory, and then systematically discussed the research progress on the existing blockchain research based on auction theory as well as auction research enabled by blockchain. Toward the end, we presented several open research issues and directions, aiming to provide useful guidance and reference for future research efforts.