The theory of reconnection in two dimensions is now fairly well understood and is highly developed, and, as we have seen, the type of reconnection that is produced depends very much on the reconnection rate, the configuration, the boundary conditions, and the parameter values. Many questions do remain, however, such as: what are the properties of turbulent or impulsive bursty reconnection; why does the diffusion region in Petschek reconnection lengthen when the resistivity is uniform; what is the effect of outflow boundary conditions on fast reconnection; how does reconnection occur in a collisionless plasma; and how do the different terms in the energy equation such as radiation and conduction affect reconnection?

The theory of three-dimensional reconnection is much less developed. We have only just started a voyage of discovery that will last many years, but some important directions have already been indicated. Many features are quite different in three dimensions. For example, we discuss here the definition of reconnection (§8.1), the structure of null points (§8.2), the nature of the bifurcations (§8.3), the global magnetic topology (§8.4), and the nature of the reconnection itself (§§8.6, 8.7).

In this chapter we introduce several new concepts. At null points, magnetic reconnection can take place by spine reconnection, fan reconnection, or separator reconnection (§8.6). Regions where magnetic field lines touch a boundary and are concave towards the interior of the volume are referred to as bald patches (§8.4.1). When no null points or bald patches are present, the mapping of field lines from one boundary to another is continuous, so they all have the same topology and there are no separatrices.