Space-air-ground-sea integrated networks (SAGSINs) are promising to offer ubiquitous Internet services across the globe while confronting research challenges such as security vulnerabilities, privacy leakage concerns, and difficulty in resource sharing. On one hand, emerging network slicing and network softwarization technologies can fulfill diverse requirements with the provision of various services on top of heterogeneous SAGSIN hardware and software resources. On the other hand, blockchain and smart contracts can compensate for network slicing and softwarization to offer secure and automatic network services. This article presents an investigation on the convergence of blockchains with network slicing and network softwarization technologies for SAGSINs from the perspectives of network management and brokerage services of SAGSINs. In contrast to existing studies, this article is the first to incorporate blockchains into network slicing and network softwarization dedicated for SAGSINs. This article starts with a summary of key characteristics and challenges of SAGSINs. Then a review of network slicing and network softwarization is given in the context of SAGSINs. This article next presents an integrated framework of network slicing, network softwarization, and blockchain for SAGSINs. Moreover, this article outlines a set of open issues and research challenges that would be useful to guide future research in this area.