Author:ViddittoAbstract:Here, I review some recent works on magnetism of cool, main-sequence stars, their winds and potential impact on surrounding exoplanets. The winds of these stars are very tenuous and persist during their lifetime. Although carrying just a small fraction of the stellar mass, these magnetic winds carry away angular momentum, thus regulating the rotation of the star. Since cool stars are likely to be surrounded by planets, understanding the host star winds and magnetism is a key step towards characterisation of exoplanetary environments. As rotation and activity are intimately related, the spin down of stars leads to a decrease in stellar activity with age. As a consequence, as stars age, a decrease in high-energy (X-ray, extreme ultraviolet) irradiation is observed, which can a ect the evaporation of exoplanetary atmospheres and, thus, also altering exoplanetary evolution.