The vague, but useful, Lefschetz Principle says that whatever in algebraic geometry is true for the complex numbers is true for all algebraically closed fields of characteristic zero, and for all algebraically closed fields of sufficiently large finite characteristics.A model-theoretic analysis is often given in terms of ultraproducts of fields of finite characteristic. Now, such ultraproducts can be construed (noncanonically) as being of nonstandard prime characteristic p and they carry a corresponding map (Frobenius) of exponentiation to power p. It turns out, very remarkably, that the properties of these maps are very linked to the Weil Conjectures, and to classical problems of Jacobi in difference algebra. In fact, "generic" difference algebra coincides with the theory of these Frobenius maps. This is work of Hrushovski and Macintyre. I will also discuss the model theory of Witt's famous lifting of Frobenius to characteristic zero, and what becomes of the Lefschetz Principle here.This is work of Belair,Scanlon and Macintyre.