Several structures taller than Burj Khalifa have started construction, but none have finished construction and none are currently under construction.

1. Nakheel Tower, also in Dubai (United Arab Emirates), started construction in 2008, even before Burj Khalifa finished construction, but never actually rose above ground. It's construction was limited to ground works. If completed, it would become the tallest building in the world with over 1000m in height and 200 floors.

2. Jeddah Tower, in Jeddah (Saudi Arabia), started construction in 2013, but construction halted in 2018. If completed, it would become the tallest building in the world with 1008m in height and 165 floors.

Notably, there is also a structure called Dubai Creek Tower. It started construction in 2016, but construction halted in 2020. If completed, it would become the tallest structure in the world with over 1300m in height. Note that Dubai Creek Tower is a supported tower and as such not classified as a building.
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