There's been news around Twitter of wrap party for GI Joe tonight. This means filming is just about complete!
Once the movie is in post-production, there should be a teaser trailer and official film stills within a few months.
IMDB has also added a synopsis on the page for GI Joe. It reads:
The G.I. Joe team faces off against Zartan, his accomplices, and the world leaders he has under his influence.
The movie will be released on June 29th, 2012.