There is the derived algebraic geometry program of Jacob Lurie, starting with his thesis in 2007 and building on the work of ..., Simpson, Toën-Vezzosi, etc. In the words of Lurie, this is basically "jazzing up" the foundations of algebraic geometry with homotopy theory. Lurie has written two 1000-page books called Higher Topos Theory and Higher Algebra, and a series of papers called DAG. He has already had success in applying the theory to the classical topic of elliptic cohomology.
See also this blog post by Tim Gowers and a relevant MO discussion.
(Of course, this can be viewed as an extension of Grothendieck's program from the 80's, see e.g. this MO discussion.)