  The $f(T)$ theory, which is an extension of teleparallel, or torsion scalar
$T$, gravity, is recently proposed to explain the present cosmic accelerating
expansion with no need of dark energy. In this Letter, we first perform the
statefinder analysis and $Om(z)$ diagnostic to two concrete $f(T)$ models,
i.e., $f(T)=\alpha (-T)^n$ and $f(T)=-\alpha T(1-e^{p {T_0}/T})$, and find that
a crossing of phantom divide line is impossible for both models. This is
contrary to an existing result where a crossing is claimed for the second
model. We, then, study the constraints on them from the latest Union 2 Type Ia
Supernova (Sne Ia) set, the baryonic acoustic oscillation (BAO), and the cosmic
microwave background (CMB) radiation. Our results show that at the 95%
confidence level $\Omega_{m0}=0.272_{-0.032}^{+0.036}$,
$n=0.04_{-0.33}^{+0.22}$ for Model 1 and $\Omega_{m0}=0.272_{-0.034}^{+0.036}$,
$p=-0.02_{-0.20}^{+0.31}$ for Model 2. A comparison of these two models with
the $\Lambda$CDM by the $\chi^2_{Min}/dof$ (dof: degree of freedom) criterion
indicates that $\Lambda$CDM is still favored by observations. We also study the
evolution of the equation of state for the effective dark energy in the theory
and find that Sne Ia favors a phantom-like dark energy, while Sne Ia + BAO +
CMB prefers a quintessence-like one.
