He's been keeping fans up-to-date today with tweets on the progress -
"Scarlett's first day on set in the Black Widow outfit. You've never heard a crew get so quiet so fast."
"Now shooting first scene with Tony Stark and Nick Fury."
"Stay tuned... Posting a pic."
Pic is below - looks like they are filming at (or at least near) Randy's Donuts in Inglewood (close to LAX). Was hoping for a look at that Black Widow outfit we've been hearing about! Ah well, maybe next time...
I know the photo seems sortta' worthless, but you know what they say every little bit helps. Oh, and all those people in Inglewood go get your cameras and snap a few pics for the fans.