In this talk, I will describe a novel Iwasawa theory for unramified Z_p-extensions of global function fields over an algebraically closed field of characteristic p. In this context, the p-adic slopes of Frobenius acting on the first crystalline cohomology of the associated Z_p-tower of algebraic curves provide a new kind of Iwasawa-theoretic object to study, and I will present evidence for a recent conjecture about the limiting behavior of these slopes.