  In this paper we provide a characterization of smooth algebraic varieties
endowed with a faithful algebraic torus action in terms of a combinatorial
description given by Altmann and Hausen. Our main result is that such a variety
X is smooth if and only if it is locally isomorphic in the \'etale topology to
the affine space endowed with a linear torus action. Furthermore, this is the
case if and only if the combinatorial data describing X is locally isomorphic
in the \'etale topology to the combinatorial data describing affine space
endowed with a linear torus action. Finally, we provide an effective method to
check the smoothness of a Gm-threefold in terms of the combinatorial data.
