A brief review is given of the theory of magnetic reconnection in three dim
ensions. The key elements of a three-dimensional null point are its spine a
nd its fan, which consist, respectively, of a field line and a surface of f
ield lines that pass through the null, The fans of two nulls intersect in g
eneral in a field line called a separator that joins the nulls. Several dif
ferent types of reconnection have been proposed. namely: spine reconnection
, fan reconnection, separator reconnection and quasi-separatrix layer recon
nection. In addition, a new exact solution for reconnective annihilation ha
s been recently discovered. A summary is also given of the impressive evide
nce of reconnection at work on the Sun provided by a range of observations
from the Yohkoh and SOHO satellites, both of solar flares and of coronal he
ating events.