My impression is that one of the celebrated results of class field theory the [principal ideal theorem][1] namely that given a number field $K$ and its maximum unramified abelian extension L, every ideal in the ring of integers $O_K$ of $K$ becomes principal in the ring of integers $O_L$ of $L$. That is, given an ideal in $I$ in $O_K$, the ideal $I \dot O_L$ is principal. 

This result was originally conjectured by Hilbert in 1900 and reduced to a group theoretic question by Artin which was finally solved by Furtwangler in 1930.

I've never seen any further discussion of the principal ideal theorem - I don't know any generalizations or applications. 

As James Milne comments in Remark 3.20 of the fifth chapter of his book on class field theory it's easy to see that there is *some* finite extension of $K$ for which all ideals of $K$ become principal. He further comments that this extension need not be the Hilbert class field of $K$ (though I haven't seen an illustrative example). 

Is the principal ideal theorem primarily of historical interest (e.g. because it was a long standing conjecture of Hilbert)? Or does it have some deeper significance?

  [1]: http://en.wikipedia.org/wiki/Principal_ideal_theorem