The tallest building in the world is currently Burj Khalifa in Dubai. It is 829.84 m high and by quite a margin the tallest structure ever built. It was completed in 2010 and is somewhat unusual. The title “tallest freestanding structures” up until then was mostly held by towers. Between 1976 and 2007 for example the CN Tower in Toronto Canada held the title "tallest structure" with a total height of 553.3 meters.
Besides the tallest structures there are various categories for buildings; highest roof, highest occupied floor, and the world's highest public observation deck for example. Also the antenna is sometimes included but only when it is part of the architectural height. We also distinguish between structures, freestanding structures and buildings. The latter is the least confusing so we include the top three of the tallest buildings here.
The Burj Khalifa is unsurpassed. The second highest building in the world is the Abraj Al Bait in Mecca, Saudi Arabia (601 m) followed by the Taipei 101 in Taipei, Taiwan with 509 meters.
The tallest building in Europe was "The Shard" in London. It is 310 meters high and was completed just before the Olympic games in London. As of November 2012 the Mercury City Tower in Moscow is Europes tallest building. It is 338 meters tall. Five of the top ten tallest buildings in Europe are in Moscow. And they do have bigger plans still. The Federation Tower in Moscow is supposed to be 506 meters tall. There was a little setback because of a fire but is is only a question of time until it will claim the title "tallest building in Europe".