I present a joint work in progress with Sho Ejiri, where we aim to prove that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism. The statement has been known for a while in characteristic zero, so our proof deals with the positive characteristic case. The previous positive characteristic results had to exclude certain wild positive characteristic behavior: wild action of Frobenius on cohomology, wild singularities of the general fibers over the Albanese image, etc.. Ours is the first result on varieties with nef anti-canonical of any dimension that avoids any such assumption. Producing such results is usually the biggest challenge in positive characteristic algebraic geometry.