Grothendieck conjectured that, for a field K finitely generated over ℚ, there exists a class of "anabelian varieties": varieties whose étale fundamental groups over K are rich enough to completely determine their geometry. He expected that the smooth anabelian varieties of dimension one should coincide with hyperbolic curves, and that "elementary anabelian varieties", varieties built from hyperbolic curves by smooth proper fibrations, should also be anabelian. The fact that hyperbolic curves are anabelian was subsequently proven by Mochizuki. In subsequent work, Hoshi generalized Mochizuki’s result to prove that certain classes of elementary anabelian varieties are, in fact, anabelian. In this talk, we will explain how to prove that elementary anabelian varieties are anabelian. Our proof uses elementary p-adic Hodge theory, a study of (log)-canonical bundles of elementary anabelian varieties, and previous results of Hoshi.