How do they manage to put those huge cranes on top of the buildings being constructed?
There are various types of cranes that are being used in construction of tall buildings and skyscrapers. One type is the self climbing crane. It is attached normally to the elevator core of the building and it attaches itself hydraulically on each level as the building progresses to the top. Another is free standing/self erecting tower crane which has a foundation for itself and is being adjusted as the construction progresses. The one they used in Burj Khalifa or Burj Dubai (tallest man-made building) is a luffing crane which is attached to the structure itself. It uses hydraulics jib to attached itself to the main structure and it goes up together with the structure.