The Sun-Earth interaction is a complex system of multi-scale processes. The spatial scales of interest vary from the mega-meter size of solar corona structures to the few hundred kilometers of the terrestrial magnetopause and even less when kinetic effects need to be considered. The temporal variations also span a wide range of scales, from thousands of years for the hydrological ocean cycles driven by the total solar radiation to scales of minutes and below for particle acceleration in magnetic reconnection. In this chapter we introduce the building blocks of the Sun-Earth system and briefly describe its important components. Solar disturbances such as solar flares and coronal mass ejection (CME) have the largest impact on geomagnetic activity, especially magnetic storms. Magnetic storms are responsible for large depressions in the horizontal (H) component of the Earth’ surface magnetic field. The strength of a storm is quantified by the Dst index, which is a local time average of the depression measured along the magnetic equator. The depression during a storm is caused by a ring current around the Earth with additional contributions from the magnetopause and tail currents. We review recent developments of empirical prediction algorithms for the Dst index using observations made upstream of the Earth, and alternative procedures based on the same concept including neural networks and the NARMAX method. Future improvements in empirical prediction will require more data from extreme events, additional physical insight to identify the role of other processes, and better measurements of the inputs to the system.