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.
(Of course, this can be viewed as an extension of Grothendieck's program from the 80's, see e.g. this MO discussion.)