Elite: Dangerous launched in December last year, but it'll be many more years before the entire galaxy has been mapped. The game takes place in a one-to-one recreation of our Milky Way galaxy, something that will take lifetimes to explore.
There are over 400 billion star systems to explore, but with part of the leveling mechanic in the game incentivising exploration of unknown star systems, Elite: Dangerous is being mapped quickly. At the current rate of exploration, Elite: Dangerous' playerbase is visiting 17,585 new star systems each day. This breaks down into 732 per hour, or 12 per minute.
If this rate continues and there isn't an influx of players in the short term, it would take a gigantic 150,895 years to map the entire galaxy. The developer behind the game is running a content for the first player to reach Elite status in exploration, giving away a $1500 prize. The first player to reach Elite in all three statuses will receive $15,000.