What is the theory behind active noise cancellation?

In a previous question, I had asked Why can't I simply negate the source time domain amplitude values to produce a destructive noise signal?

One of the posters said that while simply producing a inverses polarity (negated) signal will work in theory, in practice it is not possible

So I am asking, what is the fundamental approach (in a sort of semi technical way) to active noise cancellation?

Secondly, why are most literature on this topic in frequency domain?

It's rather simple.

By the time you send your inverted signal, the noise has already been heard.

You need to look at what frequencies are being generated, and then produce the appropriate inverted signals of those to cancel them out.