Theories of Superconductivity
Once superconductivity had been discovered the rush was on to explain what was going on. During the 1950's two separate models were postulated. In 1950 the Ginzburg-Landua theory and in 1957 the BCS theory.
The Ginzburg-Landua theory is a macroscopic, mathematical theory. It is actually a model which takes into account all the effects that are encountered on a macroscopic level, plugs them into a formula and can be used to predict how a superconductor will behave.
However this theory does not actually explain why superconductivity happens. This was not explained until 1957 with the BCS theory. The BCS stands for Bardeen, Cooper and Schrieffer; the three men who thought up and worked on the theory, who were rewarded with a Nobel Prize in 1972.
The theory is quite complicated, and quite hard to explain without going into a high level of detail. But essentially it says that: As an electron is travelling through a lattice it attracts the positive charge in the lattice towards itself, creating a distortion in the lattice. This, in turn, attracts an electron with opposite spin to the area of high positive charge. The two electrons can then be bound together to form a Cooper pair. This pair of electrons is now essentially a Boson, and behaves differently than if they were single electrons. They can resist 'bumping' into other parts of the lattice and so there is less resistance. It can also resist vibrations in the lattice, since is more stable than a single electron.
BCS theory however only explains type I, or low temperature, superconductors. No one theory has fully explained type II, high temperature superconductors. It is generally considered that there is a Nobel Prize for anyone who can.