Critical infrastructure systems are vital to underpin the functioning of a society and economy. Due to the ever-increasing number of Internet-connected Internet-of-Things (IoT)/Industrial IoT (IIoT), and the high volume of data generated and collected, security and scalability are becoming burning concerns for critical infrastructures in industry 4.0. The blockchain technology is essentially a distributed and secure ledger that records all the transactions into a hierarchically expanding chain of blocks. Edge computing brings the cloud capabilities closer to the computation tasks. The convergence of blockchain and edge computing paradigms can overcome the existing security and scalability issues. In this article, we first introduce the IoT/IIoT critical infrastructure in industry 4.0, and then we briefly present the blockchain and edge computing paradigms. After that, we show how the convergence of these two paradigms can enable secure and scalable critical infrastructures. Then, we provide a survey on the state of the art for security and privacy and scalability of IoT/IIoT critical infrastructures. A list of potential research challenges and open issues in this area is also provided, which can be used as useful resources to guide future research.