Space Weather is the branch of Space Physics that studies the relationship between the Sun variability and the dynamics of the near-Earth environment, which is in turn determined by the interaction between plasma and electromagnetic fields.

Space Weather aims at building predictive models to forecast conditions that are harmful for satellites and electric networks, due to the presence of highly energetic particles. The safeguarding of such infrastructure has an enormous economical and societal importance.

Plasma Physics is characterized by the coexistence and the interdependence of large and small-scale phenomena, typically with a scale separation of several orders of magnitude.

In this talk I will discuss some numerical techniques to tackle multiscale plasma physics simulations, with an emphasis on the coupling between fluid and kinetic scales.