  The magnetic field in many astrophysical plasmas -- such as the Solar corona
and Earth's magnetosphere -- has been shown to have a highly complex,
three-dimensional structure. Recent advances in theory and computational
simulations have shown that reconnection in these fields also has a
three-dimensional nature, in contrast to the widely used two-dimensional (or
2.5-dimensional) models. Here we discuss the underlying theory of
three-dimensional magnetic reconnection. We also review a selection of new
models that illustrate the current state of the art, as well as highlighting
the complexity of energy release processes mediated by reconnection in
complicated three-dimensional magnetic fields.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics;Plasma Physics;Space Physics