Ultraproducts of finite fields (pseudofinite fields) have been studied by model theory extensively. Lots of asymptotic qualitative behaviors of finite fields have been discovered through this way. On the other hand, the model companion of difference fields (fields with a distinguished automorphism) has also been well understood. The theory is called ACFA. It is widely believed that non-trivial ultraproducts of \bar{F_p} with frobenius are models of ACFA by an unpublished paper of Hrushovski. However, (non-trivial) ultraproducts of finite fields with Frobenius remain model-theoretically mysterious. In this talk, I will present some attempts and conjectures towards understanding them.