The paper discusses some challenges caused by application of Internet of Things (IoT) technologies and Big Data analysis (BDA) in safety critical domains such as Nuclear Power Plants (NPPs), energy grids, health systems and others. Concepts of safety and cyber safety considering security and cyber security attributes for such applications are analysed. The methodological and practical issues of implementing BDA and IoT systems and tools in context of safety and security assessment and assurance are discussed. It's suggested an extended concept of IoT as a (X)Io(Y)Z, where X and Y are adjectives determining main required attribute (X) system and attribute (Y) of generalized thing Z (business, cars, drones, etc). The benefits and limitations of application of BDA and IoT based technologies in safety critical systems are analysed including possibilities of their use for avoiding, monitoring and minimizing consequences of severe accidents. Limitations of BDA application are caused by extensive nature of technologies for collecting and processing big data. Essentially such technologies aren't green, safe and secure and it's required deep analysis of deficits, first of all, cyber security and safety before their usage. The paper describes industrial cases, where IoT and BDA are applied such as Internet of Drones based NPP accident monitoring system, IoT based monitoring and control system, system for prediction of software dependability. The recommendations and limitations of BDA and IoT application in safety critical systems are formulated.