Theory of Constraints is the most simple and yet robust manufacturing operations methodology I am aware of. It is tried-and-tested and was effectively built from the ground up (like Math was). It was developed as Eli when he was exposed to manufacturing and saw there was a real gap and the majority of the management decisions were gut-feel. His aim was to develop the science of manufacturing and I strongly believe that's what he did, taking all passion and abstract away to enable FOCUS.
In short, TOC is a mechanism to enable a manufacturing company to Focus on the key areas to drive a system as a whole forward and not to look at pieces in isolation - to evaluate the whole company.
He tackled many sub-fields including:
TOC does not replace Lean or Six-Sigma at all, as these valuable tools covered (control charts, Kanban etc.) are tackled
An image representation here but the best (quick) analogy I can think of is TOC is the compass of the ship and Lean & SixSigma the rowing oars - without the compass, the resources of the company could be heading to India instead of Iceland & wasting a lot of time and effort along the way! TOC is the focusing mechanism that Lean & Six Sigma lacks in normal manufacturing which was part of the DNA of the original Japanese implementers of these strategies (e.g. TPS & TQM) that they did not need to document this.
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