The choice of the spin-trap that is to be applied in any EPR study represents the crossroad between a comprehensive investigation and an "ordinary" quantification of production of radicals. So, the scope of our study was to compare the performance of different spin-traps for qualitative analysis of radical-generating systems, and their ability to recognize previously unnoticed radicals. In addition, we present a brief account of the difficulties involved in the detection of oxygen-centered radicals in chemical and biological systems accompanied by the rationale for using the EPR spin-trapping technique in quantitative studies of such reactive species. Certain technical aspects of EPR experiments related to efficient trapping of free radicals in biochemical systems are also discussed. As an example we present here results obtained using EPR spectroscopy and the spin-trap DEPMPO, which show that the Fenton reaction, as well as various biological systems generate a previously unappreciated hydrogen (*H) atom.