Since 1993 and 1996, the world's largest telescopes have been the twin 10-meter Keck reflectors in Hawaii. (At least that's true if by "world's largest telescope," you mean "world's largest general-purpose, single-mirror-like, optical telescope.") Next year the Kecks will be edged out by Spain's 10.4-meter GranTeCan in the Canary Islands. And the Large Binocular Telescope (LBT) in Arizona, with its twin 8.4-meter mirrors on a single mount, is coming online soon too. But much bigger things are in the works.
There's the Caltech / University of California Thirty Meter Telescope (TMT), scheduled for completion in 2016 if all goes well. And this morning, a consortium of US universities and institutions announced that a site has been chosen for the Giant Magellan Telescope (GMT). This one will consist of seven 8.4-meter mirrors grouped in a rosette on a single mount, sending light to a single focus. It'll have the light-collecting area of a 22-meter aperture. The GMT will be built at Cerro Las Campanas in the Chilean Andes, which is already a major observatory site with well-developed infrastructure.
Like the TMT, the GMT is supposed to be finished in 2016. Don't get 'em confused.
If the name Magellan is familiar, that's because of the Carnegie's Institution's two 6.5-meter Magellan Telescopes currently in operation at Las Campanas.
Once upon a time, astronomers routinely said that the 5-meter (200-inch) Hale Telescope on Palomar Mountain in California — opened in 1948 — would be the largest ever built on Earth's surface. This made sense when Earth's atmospheric seeing (the shimmering and blurring of high-power telescopic images due to tiny, ever-present heat waves) was an intractible problem. The breakthrough that made monster apertures worth building came not just from modern optical manufacturing methods, but from adaptive optics: cutting-edge technology to cancel out every little atmospheric distortion, across an entire aperture, hundreds of times a second.
The best, most versatile adaptive-optics systems use lasers to create artificial reference stars at the top of the atmosphere. These press 21st-century technology to its limit. Not to mention budgets. But they work, and astronomy is going to enter deep new realms as a result.