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The whole set of complex effects of the radiation and the plasma stream from the Sun on the Earth and her magnetosphere, our technological systems, our climate and the people determines most of the so-called space weather. The explosions that occur frequently on the Sun and especially the magnetic plasma clouds – the coronal mass ejections (CMEs) – associated to them are the most important solar drivers of the space weather. The detectable effects on Earth appear in a broad spectrum of time and length scales and have various harmful effects for human health and for our technologies. Polar light (aurora) is one of the nicest and least harmful space weather effects but alas, the space weather can also have less amusing effects on Earth. Bad weather conditions in space can hinder or damage satellite operations and communication and navigation systems and even cause power grid outages leading to a variety of tremendous socio-economic losses. Moreover, it causes radiation risks for the crew and passengers on air planes and astronauts in space. Finally, it can influence global climate changes, which is of topical interest today.

Since the space weather effects on Earth are mainly determined by the Sun, we will first say something about the most important features of this star. Then we briefly discuss the effects of space weather on Earth. Finally, we search for the causes or sources of the space weather and we focus on the scientific research and the mathematical modeling of the space weather that aims at improving the daily predictions and forecasts.