  We give a modern proof of the Regularization Theorem of Andr\'e Weil which
says that for every rational action of an algebraic group $G$ on a variety $X$
there exist a variety $Y$ with a regular action of $G$ and a $G$-equivariant
birational map $X \to Y$. Moreover, we show that a rational action of $G$ on an
affine variety $X$ with the property that each $g$ from a dense subgroup of $G$
induces a regular automorphism of $X$, is a regular action.
