Magnetic reconnection is an important plasma-physics process associated with a rapid change of magnetic field topology. It often leads to a violent release of magnetically-stored energy and thus powers many of the most spectacular and energetic phenomena in laboratory, space, and astrophysical plasmas. In this talk, I will review the present status of our knowledge of magnetic reconnection, with an emphasis on the transition from the slow collisional to the fast collisionless reconnection regime. I will then describe some of its important solar- and astrophysical applications and will show how the application of the recent advances in reconnection research can help us understand the heating of the solar and black-hole accretion-disk coronae. I will conclude by outlining some of the important open questions and the directions of future research, including the effects of turbulence and plasmoid formation in long current sheets.