Geospace is very sensitive to solar activity, to changes in solar activity, and to its manifestations in the near-Earth space environment and on the Earth. Indeed, the Sun is the source of heat and life that maintains life as we know it here on Earth. However, the Sun is also the origin of various radiation (electromagnetic and particles) that can be a threat to humans and to all kinds of human activities (technological and biological). The effect of space radiation on humans is a potential showstopper to human space exploration. More controversial is the question of whether the geomagnetic environment when disturbed can have either direct or indirect effects on human health and physiology even when the magnitude of the disturbance is small. Heliobiology is the branch of science that deals with the impact of solar activity on living organisms. This paper considers the possible effects of solar and geomagnetic variability on certain biological and ecological systems situated on Earth by performing a review of thematically selected papers and recently obtained results of cross-disciplinary heliobiological studies carried out by different research groups. Physiological measurements (blood flow, arterial blood pressure, heart rate, etc.) and their comparison with solar and geomagnetic disturbances are presented. Changes in cardiac health-state and its parameters in relation to changes in environmental physical activity are discussed. The sensitivity of newborns to changes in the environment is considered using physiological parameters. Influenza epidemics and pandemics, as well as potential effects on animals of geomagnetic activity, are also discussed. General conclusions, based on the results of original researches and of this review, are given.