Since the discovery of the enigmatically hot layer in the Sun, the solar corona, the problem of its heating had remained elusive. Over the last 60 years we learned that the solar corona is not just hot .quiet. plasma, but a highly .emotional. place for the most violent eruptions in the solar system, occurring on scales from hundreds to hundreds of thousands of kilometers. The recent solar missions, SOHO, TRACE and Hinode provided crucial clues for resolving the long-standing problem of the solar coronal heating. Meanwhile, the space missions, HST, Chandra, FUSE, XMM-Newton, have confirmed that hot and X-ray bright coronae exist not only in the Sun, but in stars ranging from young pre-main sequence stars to evolved giants. These new data raise one fundamental question in astrophysics: can the solar analogy be directly applied to other stars, and how do the underlying physical processes differ? In this review I will discuss recent observations of the solar and stellar coronae and the physical mechanisms involved in their heating.