In the last decade, the development of more compact and lightweight radiation detection systems led to their application in handheld and small unmanned systems, particularly air-based platforms. Examples of improvements are: the use of silicon photomultiplier-based scintillators, new scintillating crystals, compact dual-mode detectors (gamma/neutron), data fusion, mobile sensor networks, cooperative detection and search. Gamma cameras and dual-particle cameras are increasingly being used for source location. This study reviews and discusses the research advancements in the field of gamma-ray and neutron measurements using mobile radiation detection systems since the Fukushima nuclear accident. Four scenarios are considered: radiological and nuclear accidents and emergencies; illicit traffic of special nuclear materials and radioactive materials; nuclear, accelerator, targets, and irradiation facilities; and naturally occurring radioactive materials monitoring-related activities. The work presented in this paper aims to: compile and review information on the radiation detection systems, contextual sensors and platforms used for each scenario; assess their advantages and limitations, looking prospectively to new research and challenges in the field; and support the decision making of national radioprotection agencies and response teams in respect to adequate detection system for each scenario. For that, an extensive literature review was conducted.