TITLE: Windows into new mathematical worlds
QUESTION [7 upvotes]: Yitang Zhang's Annals of Mathematics primes-gap result
opened a new window, which 
Polymath's reduction from $70\times 10^6$ to $246$ attests.
Perhaps
Harald Helfgott's
celebrated proof of the odd Goldbach's conjecture
has not similarly open new avenues—or at least not yet.
Certainly the Green-Tao theorem has opened new windows.
Perhaps the
Guth-Katz breakthrough on the Erdős distance problem
has opened new windows.
My question is, 

Q. Which results in the recent past (~last decade+) have opened 
  significant windows into new mathematics?

I realize this is quite subjective,
but it requires a high-level view of fields of mathematics
to notice this while it is happening, in a way that others (like me) without that
expertise cannot discern.
It would be educational to learn of expert opinions, without diminishing
the significance of any particular result.
Rather I am hoping for a celebration of those results which seem not to be
the end of a line of investigation, but rather a new beginning.

REPLY [7 votes]: The work of Lurie, and others (for instance, Rezk, Joyal, and also older work of Toen, Vezzosi, Simpson, ...) on Higher Topos Theory and Higher Algebra, leading to e.g. a proof of the cobordism hypothesis (see also Freed's article) and the proof of the Weil conjecture on Tamagawa numbers for function fields over finite fields. 
I'm making this community wiki so others can add things.