Let T be an algebraic torus, over a field k. Endo and Miyata found a criterion, to determine whether or not T is a stably rational k-variety. Voskresenskii conjectured that T is k-rational, if it is stably k-rational. We will concentrate on two aspects of this topic, and then attempt to relate them.

1.The recent work of Hoshi and Yamasaki, for norm one tori arising from a dihedral extension.

2. An explicit proof of Klyachko's Theorem, stating that Voskresenskii's conjecture holds for an interesting class of tori.