Many astrophysical and laboratory plasmas have a very high conductivity. In the limit of infinite conductivity the magnetic field is “frozen” to the plasma, and consequently the magnetic field topology (defined by the connectivity and linkage of the field lines) is preserved. A breakdown in this “ideal” behaviour permits “magnetic reconnection” to occur, which is behind explosive energy release processes such as solar flare and sawtooth crashes in tokamaks. There exist analogous processes in high Reynolds number fluids and superfluids. Here I will develop the mathematical basis for understanding these concepts. I will also provide some illustrative examples of the importance of characterising magnetic complexity in determining where and how magnetic reconnection occurs.