A systematic review of heliobiological studies of the last 25 years devoted to the study of the potential influence of space weather factors on human health and well-being was carried out. We proposed three criteria (coordinates), according to which the work on solar–biospheric relations was systematized: the time scale of data sampling (years, days, hours, minutes); the level of organization of the biological system under study (population, group, individual, body system); and the degree of system response (norm, adaptation, failure of adaptation (illness), disaster (death)). This systematic review demonstrates that three parameters mentioned above are closely related in the existing heliobiological studies: the larger the selected time scale, the higher the level of estimated biological system organization and the stronger the potential response degree is. The long-term studies are devoted to the possible influence of solar activity on population disasters, i.e., significant increases in morbidity and mortality. On a daily scale, a probable effect of geomagnetic storms and other space weather events on short-term local outbreaks of morbidity is shown as well as on cases of deterioration in people functional state. On an intraday scale, in the regular functioning mode, the heart and brain rhythms of healthy people turn to be synchronized with geomagnetic field variations in some frequency ranges, which apparently is the necessary organism’s existence element. The applicability of different space weather indices at different data sampling rates, the need to take into account the contribution of meteorological factors, and the prospects for an individual approach in heliobiology are discussed. The modern important results of experiments on modeling the action of magnetic storms in laboratory conditions and the substantiation of possible theoreical mechanisms are described. These results provide an experimental and theoretical basis for studies of possible connections of space weather and human health.