  Recently cosmological dynamics of anisotropic Universe in $f(T)$ gravity
became an area of intense investigations. Some earlier papers devoted to this
issue contain contradictory claims about the nature and propertied of vacuum
solutions in this theory. The goal of the present paper is to clarify this
situation. We compare properties of $f(T)$ and $f(R)$ vacuum solutions and
outline differences between them. The Kasner solution appears to be an exact
solution for the $T=0$ branch, and an asymptotic solution for $T \ne 0$ branch.
It is shown that Kasner solution is the past attractor if $T<0$, being past and
future attractor for $T>0$ branch.
