The activity of stars such as the Sun varies over timescales ranging from the very short to the very long—stellar and planetary evolutionary timescales. Experience from our solar system indicates that short-term, transient events such as stellar flares and coronal mass ejections create hazardous space environmental conditions that impact Earth-orbiting satellites and planetary atmospheres. Extreme events such as stellar superflares may play a role in atmospheric mass loss and create conditions unsuitable for life. Slower, long-term evolutions of the activity of Sun-like stars over millennia to billions of years result in variations in stellar wind properties, radiation flux, cosmic ray flux, and frequency of magnetic storms. This coupled evolution of star-planet systems eventually determines planetary and exoplanetary habitability. The Solar Evolution and Extrema (SEE) initiative of the Variability of the Sun and Its Terrestrial Impact (VarSITI) program of the Scientific Committee on Solar-Terrestrial Physics (SCOSTEP) aimed to facilitate and build capacity in this interdisciplinary subject of broad interest in astronomy and astrophysics. In this review, we highlight progress in the major themes that were the focus of this interdisciplinary program, namely, reconstructing and understanding past solar activity including grand minima and maxima, facilitating physical dynamo-model-based predictions of future solar activity, understanding the evolution of solar activity over Earth’s history including the faint young Sun paradox, and exploring solar-stellar connections with the goal of illuminating the extreme range of activity that our parent star—the Sun—may have displayed in the past, or may be capable of unleashing in the future.