TITLE: Most important mathematical results in last 30 years
QUESTION [10 upvotes]: Which results from the last 30 years, in any area of mathematics, do you think are the most important ones?
Specifically, which are the ones that will have more impact across all math and/or settle significant questions, in your opinion? It does not matter if they are big, lond-proofed results like a classification theorem, or little, elementary lemmas proved in a paragraph.
To keep this reasonable, I propose that every contributor posts at most 10 results.
Please, write one result per post, so that we can all vote properly and have a real ranking afterwards. Also, please don't just write the name, write a little description (hopefully, self-contained) and put some link if desirable.
(My personal aim with this question is to learn. I hope to be a bit better versed  after studying your answers!)

REPLY [6 votes]: Perelman's proof of the Geometrization conjecture (see here, here and here) was the crowning achievement of decades of work.  It was the most important of Thurston's conjectures about the topology of 3-manifolds.
Oh, and I nearly forgot to mention that the Poincare Conjecture is a consequence.

REPLY [5 votes]: Agol's proof of the Virtual Haken conjecture was a wonderful application of the tools developed by Wise and his coauthors in geometric group theory to 3-manifold topology.  The Virtual Haken conjecture, which can be thought of as the topological classification of compact 3-manifolds, is a fundamental result.
Agol's theorem:

Every cubulable hyperbolic group is virtually special.

also has other dramatic consequences for hyperbolic groups.  It's arguably the most important theorem proved in both algebra and topology in the last five years.

REPLY [3 votes]: Kahn--Markovic's proofs of the Surface Subgroup conjecture and the Ehrenpreis conjecture.