In reply to some suggestions earlier in the thread, there is no way Rautavaara's 7th Symphony, 3rd Movement, is atonal. Neither is most of Messiaen's Quartet for the End of Time. It's harmony that's free of the grip of tonality, and when combined with texturalism (made possible by modern technology), I believe these will be the two main elements when the real 21st century movement starts to define itself.

I put the Rautavaara on the list to counter the myth that 12-tone music has to be dissonant and cerebral -- any average art music listener can at least appreciate this movement (it's quite seductive if I do say so). The symphony as a whole is a lot like Berg's Violin Concerto in that the row is constructed specifically to create tonal sonorities, and that it moves into and out of 12-tone organization seamlessly. The sonorities formed by the Rautavaara row are traditional, but their motion/direction is determined by the row and row succession rather than functional harmony. Get a score and do a 12-tone analysis -- it's quite fascinating!
Messiaen uses a variety of pitch organization methods in the Quartet, including lots of modes of his own creation and combinations of these modes (multi-modal I assume one can call this), as described in his "Technique of my Musical Language." Some of the sappier movements (the violin/piano and cello/piano movements, for example) again can resemble traditional tonality in a purely vertical manner, but again chord succession is on the whole not that of functional tonality.
As for what you call "texturalism", I would say I have encountered far too many fellow composers who favor this dimension because they have such a poor understanding of the more traditional "structural" aspects of music (i.e. pitch, rhythm, harmony, counterpoint, etc.). On the other hand there are also composers who are so focused on structural aspects that their textures and orchestration become so bland. Time will tell where the 21st century is going (I neither agree nor disagree with your statement), but one cannot doubt that what were once considered secondary elements (texture and orchestration for example) have risen to a level as great as traditionally structural elements.