Heating in the solar atmosphere

The solar coronal plasma, mainly confined in magnetic flux tubes, is maintained at temperatures of several millions of K. The heating process that generates and sustains the hot corona has so far defied a quantitative understanding despite efforts spanning over half a century. In this paper I review the most popular and viable mechanisms of heating the solar atmosphere, from low chromospheric levels through the transition region up to the corona. I address two principal questions: What is the source of plasma heating in the solar (and stellar) atmosphere? How do perturbations dissipate efficiently, resulting in hot plasmas? The latest results of theoretical and observational studies provide some answers, but there remains much to be learned.