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.