Part of the population considers themselves as sensitive to the man-made electromagnetic radiation (EMF) emitted by powerlines, electric wiring, electric home appliance and the wireless communication devices and networks. Sensitivity is characterized by a broad variety of non-specific symptoms that the sensitive people claim to experience when exposed to EMF. While the experienced symptoms are currently considered as a real life impairment, the factor causing these symptoms remains unclear. So far, scientists were unable to find causality link between symptoms experienced by sensitive persons and the exposures to EMF. However, as presented in this review, the executed to-date scientific studies, examining sensitivity to EMF, are of poor quality to find the link between EMF exposures and sensitivity symptoms of some people. It is logical to consider that the sensitivity to EMF exists but the scientific methodology used to find it is of insufficient quality. It is time to drop out psychology driven provocation studies that ask about feelings-based non-specific symptoms experienced by volunteers under EMF exposure. Such research approach produces only subjective and therefore highly unreliable data that is insufficient to prove, or to disprove, causality link between EHS and EMF. There is a need for a new direction in studying sensitivity to EMF. The basis for it is the notion of a commonly known phenomenon of individual sensitivity, where individuals' responses to EMF depend on the genetic and epigenetic properties of the individual. It is proposed here that new studies, combining provocation approach, where volunteers are exposed to EMF, and high-throughput technologies of transcriptomics and proteomics are used to generate objective data, detecting molecular level biochemical responses of human body to EMF.