I will focus on nonlocal models of inflation, exemplified by p-adic string
theory, which have novel features including H exceeding the string scale, slow
roll despite a steep potential, and observably large nongaussianity. In passing
I will mention other recent results: evidence for a bump in the CMB at l ~ 500,
and how double hybrid inflation could explain it; the possibility of observing
modifications to the Friedmann equation from inflation in a 6D braneworld
through breaking the tensor-to-scalar consistency relation.