  We give a short survey of the rationality problem for quasi-monomial actions
which includes Noether's problem and the rationality problem for algebraic
tori, and report some results on rationality problem in three recent papers
Hoshi, Kang and Kitayama [HKKi], Hoshi, Kang and Kunyavskii [HKKu] and Hoshi
and Yamasaki [HY].
