The Ref can call for a review if he is not sure if one of the rules was violated on a goal, or the review booth can call down to the Ref, and review a goal. Once a face-off has happened, and the game continues the goal cannot be reviewed.
Reviews can happen when:
To see if the puck crossed the goal line. Was it kicked in. Was it a high stick. Was it put in with a hand. Was it in before the clock ran out.
Not before the Whistle went. That is a discretionary call by the Ref. If his intent was that he was about to blow the whistle, then it is not reviewable...
The other I believe was if it goes in directly off an official. This happened the other day, and the goal was waived off, but I am not sure if they would review it.