The transition of the Internet from IPv4 to IPv6 is urgent and inevitable. A series of IPv6 transition solutions have been proposed by the Internet Engineering Task Force; yet most of them have not seen success in real world, and some were even obsoleted. Nowadays IPv6 transition solutions are still continuously being worked out. The major difference among these solutions is the state management, which is an essential function and has a profound influence on many aspects of networking, such as addressing, provisioning, and network performance. In this article, we present a comprehensive survey on IPv6 transition solutions from the perspective of state management. We first briefly review the basic rationale of IPv6 transition solutions, highlighting the necessity of state management. Then we study various types of state management adopted by typical IPv6 transition solutions, focusing on their impacts on aspects of networks. Based on the above analyses, we summarize the applicability of different types of state management, and discuss their state-of-the-art application directions that may lead to potential future research directions in the IPv6 transition process.