  In this article we survey the basic properties of $p^{-e}$-linear
endomorphisms of coherent $\O_X$-modules, i.e. of $\O_X$-linear maps $F_* \sF
\to \sG$ where $\sF,\sG$ are $\O_X$-modules and $F$ is the Frobenius of a
variety of finite type over a perfect field of characteristic $p > 0$. We
emphasize their relevance to commutative algebra, local cohomology and the
theory of test ideals on the one hand, and global geometric applications to
vanishing theorems and lifting of sections on the other.
