Let $X$ be an algebraic variety over an algebraically closed field of positive characteristic $p$ with the Frobenius morphism $F : X /to X$. For each integer $e>0$, we can consider the push-forward $F^e_*O_X$ of the structure sheaf of $X$ by the $e$-times iterate of the Frobenius, which is a coherent sheaf of rank $p^{e/dim X}$ and is locally free if and only if $X$ is smooth. In this talk, I will review local and global aspects of the Frobenius push-forward, focusing on its splitting property, the F-blowup as its universal flattening, and its global structure as a vector bundle.