Blockchain was first introduced in 2009 as the technology behind the Bitcoin digital currency. It is the backbone technology for many Distributed Ledger and Distributed Computing applications, such as digital cryptocurrencies and digital smart contracts. The advantages of Blockchain-Fog integration include enhanced security, integrity, reliability, and fault-tolerance, due to the decentralization and trust management mechanisms they provide. In this talk I summarize the results we achieved in Blockchain-Fog integration, then present our current works and future directions. First, we conducted a survey to highlight the roles Blockchains played in cloud and fog systems, and presented how the corresponding research communities envisage the future Blockchain-Fog integration. Based on the identified challenges, we turned our attention to address some of these issues. To enable the development and evaluation of methods for Blockchain-Fog integration, we designed a special purpose simulator called FoBSim. By realizing such integration, a Blockchain can be placed in the fog layer, the end-user layer, or the cloud layer. The simulator is capable of investigating the differences of such placements, and their main properties for executing certain applications with different requirements. In our current works we aim at investigating Blockchain-Fog integration advantages for real-world applications. We already started to develop a Blockchain-assisted credential management system, which could be used for applications needing trustful and privacy-aware, distributed credential issuing and validation. The currently targeted use cases include international student diploma management and COVID-19 immunity passport management.