The effects of three-dimensionality on the modelling of solar magnetic
fields are described. We focus on two processes that are believed to
play an important role in coronal heating - the braiding of field line
s by photospheric motions and the reconnection of colliding Bur tubes.
First, it is shown that a proper treatment of boundary conditions at
the photosphere in 3D entails qualitatively new physical processes tha
t are not present in 2D. The numerical resolution of even simple bound
ary velocity patterns in 3D Leads to obstacles which have no counterpa
rt in the 2D case. We conclude that adaptive mesh refinement is necess
ary for capturing the essential 3D physics of a braiding motion at the
photosphere. Next, the effects of 3D on magnetic reconnection are dis
cussed. Reconnection in 3D can lead to an evolution of interacting flu
x tubes, magnetic tunneling, that is not only impossible in lower dime
nsionality, but is strikingly counterintuitive. The implications of th
ese results for the structure of the solar magnetic field and for coro
nal heating are described.