This survey points to the mechanisms of bioresponse caused by magnetic fields (MFs), paying attention to their action not only on ions, molecules and macromolecules, but also on cells, tissues and organisms. The significance of findings concerning the MF-dependence of cell proliferation, necrosis or apoptosis was judged by comparing the results obtained in a solenoid, where an MF can be added to the geomagnetic field (GMF), with those obtained in a magnetically shielded room, where the MFs can be attenuated or null. This comparative criterion was particularly appropriate when the differences detectable between the data provided by experimental samples and the data provided by control samples were rather small, as observed in estimating the MF-influence on total DNA replication, RNA transcription and polypeptide translation. The MF-induced inhibition of apoptosis was considered as a risk potentially leading to accumulation of cancer cells. The analysis also surveyed the MF-dependence of the interactions between host animal cells and infecting bacteria. In relation to studies on the origin and adaptation of life on the Earth, theoretical insights paving the way to elucidating the MF-interactions with biostructures and biosystems of different orders of organization evaluated the possible involvement of the so-called "biological windows". Analogously to what is known for ionizing radiations, the efficiency of the applied MFs appeared to depend on the complexity of their biological targets.