In music theory, we were always told that the seventh step, VII, was a "diminished" triad, which resolved up to the tonic. In the key of C major, this would be VII dim-I C major.
I didn't buy it. My ear didn't buy it, and I always trust my ear.
To me, this B-D-F always sounded like an incomplete dominant; a G7 without a root. Then, it made sense to resolve it to C like a V7-I always does.
Then I started seeing "roots" where they didn't exist, in diminished seventh chords. Like the first B-D-F, I found that I could put an imaginary root below the diminished triad, in this case a G below the B-D-F triad, and I created a dominant chord (G-B-D-F). And it worked with diminished sevenths as well; G below a B-D-F-Ab (dim 7) gives us a "flat ninth" dominant: G-B-D-F-Ab.
Later, my suspicions were confirmed by two theorists, Schoenberg (in his Harmonilehre) and Walter Piston (in his Harmony text). Both treated the resolution of any diminished chord by "imagining" a root below the lowest tone, and resolving it as if it were a typical V7-I.