The last quarter of the 20th and the first two decades of the 21st centuries are characterized by increasing hazards of electromagnetic fields for the biosphere and public health. This anthropogenic factor has been considered in two distinct directions: low frequency electromagnetic fields (EMF) from power lines and high frequency EMF from cellular communications. Public fear as well as scientific understanding have pointed to the serious problems for public health. World Health Organization (WHO) recognized the importance of this issue and originated “The international EMF project” which during the last two decades has organized a series of international meetings in different locations of the world with the intention to harmonize standards for EMF radiation and exposure. Unfortunately, this activity did not end with a more or less defined conclusion or at least a recommendation. With respect to EMF emitted for the purpose of mobile communications, the IARChas recognized the non-ionizing radiation from microwaves used in mobile communications as a possible carcinogenic source (category 2B). This paper discussed the basic physics problems related to characterization of the non-ionizing radiation that are of importance for public health. Special attention is paid to missing definitions for basic terminology and to the non-thermal effects of EMF as well as the incorrect use of SAR for defining conditions of exposure. The core of the paper is the potential hazard of mobile communications for human health.