One (not-entirely serious) possibility (with implicit spoilers), beneath the cut.

(gif via the comments thread at ComicBookMovie.com)

More seriously, I do wonder what Marvel's famed archer was up to during The Winter Soldier. I don't usually press the "where were all the other Avengers" questions in these movies, because I know it's the kind of nitpicky, detail-obsessed questioning that honestly can be kind of annoying (and besides which I don't really care that much). But in this case it does seem like a question worth asking, given Barton's role in SHIELD generally and close association with Natasha in particular.

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I've heard speculation that he was on the trail of the Maximoff twins, which would make a certain amount of sense and allow an easy lead into Age of Ultron so that doesn't seem too unlikely.