Mostly plain English intro to Magnetic Monopoles
One of the most basic properties of magnetism is that a magnet always has two
poles, north and south, which cannot be separated into isolated poles, i.e.,
magnetic monopoles. However, there are strong theoretical arguments why
magnetic monopoles should exist. In spite of extensive searches they have not
been found, but they have nevertheless played a central role in our
understanding of physics at the most fundamental level.
http://arxiv.org/abs/1204.3077
However, because no magnetic charges have been found, the duality symmetry appears to be broken. This means that, in fact, the only difference between electricity and magnetism is that electric charges exist but magnetic charges do not.
This raises the question why nature has this asymmetry. From the point of view of classical electrodynamics, there is no reason why there could not be magnetic charges, and if they did, the duality symmetry would be intact. In other words, classical electrodynamics is perfectly compatible with the notion of magnetic monopoles, and from the aesthetic point of view it is strange that magnetic monopoles do not seem to exist, because their existence would make the theory more symmetric.