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Caltech Professor of theoretical physics Sean Carroll presents a brief guide to the theory of Quantum Electro Dynamics - which underpins almost everything we see in the Universe, including all of chemistry and biology. When Quantum theory emerged physicists had to find a way to apply it to the behaviour of matter and forces. Paul Dirac was the first physicist to figure out how to apply the theory to the electron, revealing that they behaved more like fields than particles. The resulting 'fuzziness' which this picture of the world produced posed further problems for physicists by yielding infinities in their calculations which fundamentally disagreed with experimental results. Their initial reaction was to throw their theory away. That was until Richard Feynman decided to look at it from a different perspective. The resulting solutions that Feynman and others came up with put the finishing touches to the theory of Quantum Electro Dynamics - or QED - which is today the most successful theory human beings have ever come up with.