  Magnetic reconnection requires the violation of the frozen-in condition which
ties gyrating charged particles to the magnetic field inhibiting diffusion.
Ongoing reconnection has been identified in near-Earth space as being
responsible for the excitation of substorms, magnetic storms, generation of
field aligned currents and their consequences, the wealth of auroral phenomena.
Its theoretical understanding is now on the verge of being completed.
Reconnection takes place in thin current sheets. Analytical concepts proceeded
gradually down to the microscopic scale, the scale of the electron skin depth
or inertial length, recognizing that current layers that thin do preferentially
undergo spontaneous reconnection. Thick current layers start reconnecting when
being forced by plasma inflow to thin. For almost half a century the physical
mechanism of reconnection has remained a mystery. Spacecraft in situ
observations in combination with sophisticated numerical simulations in two and
three dimensions recently clarified the mist, finding that reconnection
produces a specific structure of the current layer inside the electron inertial
(also called electron diffusion) region around the reconnection site, the X
line. Onset of reconnection is attributed to pseudo-viscous contributions of
the electron pressure tensor aided by electron inertia and drag, creating a
complicated structured electron current sheet, electric fields, and an electron
exhaust extended along the current layer. We review the general background
theory and recent developments in numerical simulation on collisionless
reconnection. It is impossible to cover the entire field of reconnection in a
short space-limited review. The presentation necessarily remains cursory,
determined by our taste, preferences, and knowledge. Only a small amount of
observations is included in order to support the few selected numerical
simulations.
