Over the past two decades, there have been a series of major solar space missions, namely Yohkoh, SOHO, TRACE, and in the past 5 years, STEREO, Hinode and SDO, studying various aspects of the Sun and providing images and spectroscopic data with amazing temporal, spatial and spectral resolution. Over the same period, the type and nature of numerical models in solar physics have been completely revolutionized as a result of widespread accessibility to parallel computers. These unprecedented advances on both observational and theoretical fronts have led to significant improvements in our understanding of many aspects of the Sun's behaviour and furthered our knowledge of plasma physics processes that govern solar and other astrophysical phenomena. In this Theme Issue, the current perspectives on the main astrophysical processes that shape our Sun are reviewed. In this Introduction, they are discussed briefly to help set the scene.