Natural disasters such as earthquakes, floods, and forest fires involve critical situations in which human lives and infrastructures are in jeopardy. People are often injured and/or trapped without being able to be assisted by first responders on time. Moreover, in most cases, the harsh environment jeopardizes first responders by significantly increasing the difficulty of their mission. In such scenarios, time is crucial and often of vital importance. First responders must have a clear and complete view of the current situation every few seconds/minutes to efficiently and timely tackle emerging challenges, ensuring the safety of both victims and personnel. Advances in related technology including robots, drones, and Internet of Things (IoT)-enabled equipment have increased their usability and importance in life- and time-critical decision support systems such as the ones designed and developed for Search and Rescue (SAR) missions. Such systems depend on efficiency in their ability to integrate large volumes of heterogeneous and streaming data and reason with this data in (near) real time. In addition, real-time critical data integration and reasoning need to be performed on edge devices that reside near the missions, instead of using cloud infrastructure. The aim of this paper is twofold: (a) to review technologies and approaches related to real-time semantic data integration and reasoning on IoT-enabled collaborative entities and edge devices in life- and time-critical decision support systems, with a focus on systems designed for SAR missions and (b) to identify open issues and challenges focusing on the specific topic. In addition, this paper proposes a novel approach that will go beyond the state-of-the-art in efficiently recognizing time-critical high-level events, supporting commanders and first responders with meaningful and life-critical insights about the current and predicted state of the environment in which they operate.