In order to study algebraic varieties of positive characteristics, it is sometimes fruitful to think about their lifts to characteristic 0 or infinitesimal lifts. For example, in the work of Deligne and Illusie, an infinitesimal liftability was a key ingredient for studying the degeneration of Hodge to de Rham spectral sequence. In this talk, we will discuss a particular type of lifting of varieties where we also lift the Frobenius morphism. This “Frobenius lift” has quite strong cohomological consequences, so we expect this to be rare. In fact, a conjecture of Achinger, Witaszek and Zdanowicz predicts that smooth projective varieties with Frobenius lifts are roughly built out of toric varieties and abelian varieties, and we will illustrate this conjecture by examples.