GCHQ in the uk have been doing it for most uk traffic, and it seems the approach is to store full data as long as they can, and store headers for longer. All the content is stored for 3 days, then the headers are kept for 30 days, and shared with other agencies like the NSA, who may well keep it all indefitely if they have enough storage available. They probably do some early filtering to keep it manageable, removing duplicate content, unwanted videos etc. and the headers and metadata are probably not that large. Before reading the GCHQ docs I wouldn't have found this claim credible...

If they are not collecting every communication in the world, you can be sure it is not from lack of ambition to do so. In the words of General Alexander:

“Why can’t we collect all the signals all the time?” the N.S.A. director was quoted as saying. “Sounds like a good summer project for Menwith."

Which is a worryng thought when you realise the implications of this ambition. We used to think that only a god could be omniscient, but that is the current ambition of our intelligence services and politicians.