We investigated relations among solar activity, climate and cosmogenic radiocarbon in a time series of various astrophysical, geophysical, archaeological and historical data. We studied records of tree-ring thickness, aurora borealis, the catalog of visible sunspots, sedimentary deposits from lakes and oceans, global glacial advance and retreat chronology, polar ice cores and human migrations. In these data, we searched for evidence of medium- and long-term solar cycles. Application of different spectral techniques to the atmospheric 14C concentration time series indicates the existence of spectral lines at a few dominant periodicities ranging from 11 yr to ca. 2 ka. Different laboratories have confirmed the presence of the ca. 210-and 2000-yr spectral features in long 14C series in tree rings. The ca. 210-yr 14C cycle is probably caused by heliomagnetic modulation of the cosmic-ray flux. The extrema of both the ca. 210-yr 14C period and solar activity correlate with the cold and warm epochs of global climate, at least for the past millennium, and this correlation has the correct sign. The periods of low solar activity are well correlated with the Little Ice Ages. The cause of the ca. 2 ka 14C period is, as yet, uncertain, but evidence from the analyses of various natural records shows that it could have a solar origin. In this study, we obtained powerful manifestations of solar activity and climate warming epochs at ca. 1500, 3800, 6100, 8200, 10,500 and 12,600 bp. A similar feature occurs in epochs of minimum amplitude in the 14C content in tree rings. Thus, solar activity may affect both the 14C content in the Earth's atmosphere and climate.