When a trailer (not a teaser) comes out, the rest of the movie usually follows a few months later. Is the movie itself typically complete at this point, or is there still (post-)production work to be done?
Trailers typically come out before a movie is "distribution-ready", but exactly how far along depends on the movie, and how far in advance they want to hype it.
For starters, trailers are usually made well in advance of the final product. Keep in mind that the trailers have to go through much of the same post-production work as the film itself. The effects for CGI-heavy scenes need to be there, they have to score it (often before they've settled on the contents of the final score), they need to edit it, and even get it rated. This has to happen in time to release the trailers months out from the movie. This is why there are so often dialogue, or entire scenes, in trailers that are completely missing from the final product: the film hasn't been through editing by the time the trailers are being put together.
Whether or not they wait to release the trailer until the movie is finished is a different question. Most likely they are at least done the principle shooting and the movie's well into post-production. Once the trailers are out, the basic story, tone, look, etc. of the movie is set in the public's eye, and it's not likely they're going to change it significantly beyond then. However, it's still entirely possible that last minute pick-ups or reshoots could still be happening.