Industrial Internet-of-Things (IIoT) with massive data transfers and huge numbers of connected devices, incombination with the high demand for greater quality-of-services, signal processing is no longer producing small data sets but rather, very large ones (measured in gigabytes or terabytes), or even higher. This has posed critical challenges in the context of optimisation. Communication scenarios such as online applications come with the need for real-time optimisation. In such scenarios, often under a dynamic environment, a strict real-time deadline is the most important requirement to be met. To this end, embedded convex optimisation, which can be redesigned and updated within a fast time-scale given sufficient computing power, is a candidate to deal with the challenges in real-time optimisation applications. Real-time optimisation is now becoming a reality in signal processing and wireless networks of IIoT. Research into new technologies to meet future demands is receiving urgent attention on a global scale, especially when 5G networks are expected to be in place in 2020. This work addresses the fundamentals, technologies and practically relevant questions related to the many challenges arising from real-time optimisation communications for industrial IoT.