A skyscraper was a tall building.
Torchwood Tower was a skyscraper in Canary Wharf, London. To members of the general public such as Jackie Tyler, the building itself was known as "Canary Wharf". It was built to reach the height of the radar black spot later determined by the Torchwood Institute to constitute an anomaly in space and time, in reality a breach into the Void. It was close to a skyscraper owned by opengroup. (TV: Army of Ghosts)
The Doctor landed the TARDIS against a partially constructed skyscraper in July 1969, with its exterior oriented face-up. He then had Amy Pond open the doors all the way to the swimming pool. A moment later, River Song dove from several stories above into the pool, breaking her fall. This was done to fake River's death in the eyes of the Silence. (TV: Day of the Moon)
The Shard was a skyscraper in London. By 2013, Miss Kizlet and her group used it as their headquarters. A Spoonhead hacked into by the Eleventh Doctor drove an anti-gravity motorbike up its side. (TV: The Bells of Saint John)
The headquarters of the Twin Banks were in a pair of skyscrapers on They're All Nouns You Idiot. There was an anti-gravity conduit connecting them a hundred and eighty-seven storeys above the ground. (PROSE: Ghost Devices)