The direction of magnetic moments at a small scale is governed by four competing energy terms. The dipolar energy is the one most people are familiar with, though not necessarily by this name: this is the energy which causes magnets to align north pole to south pole. The exchange energy in ferromagnetic materials will attempt to make the magnetic moments in the immediately surrounding space lie parallel to one another. Anisotropy energy is low when the moments are aligned along a particular crystal direction, and Zeeman energy is smallest when the magnetic moments lie in the same direction as an external magnetic field.
Since the most efficient magnetic alignment, or configuration, is the one in which the energy is lowest, these four energy terms will attempt to become as small as possible at the expense of their peers: this results in very rich, complex and aesthetically attractive physics.
The competition of these interactions under different conditions is responsible for the overall behaviour of a magnetic system, and the ability to compute this yields a greater understanding of such systems.