  We investigate the observational signatures of the holographic dark energy
models in this paper, including both the original model and a model with an
interaction term between the dark energy and dark matter. We first delineate
the dynamical behavior of such models, especially whether they would have "Big
Rip" for different parameters, then we use several recent observations,
including 182 high-quality type Ia supernovae data observed with the Hubble
Space Telescope, the SNLS and ESSENCE surveys, 42 latest Chandra X-ray cluster
gas mass fraction, 27 high-redshift gamma-ray burst samples, the baryon
acoustic oscillation measurement from the Sloan Digital Sky Survey, and the CMB
shift parameter from WMAP three years result to give more reliable and tighter
constraints on the holographic dark energy models. The results of our
constraints for the holographic dark energy model without interaction is
$c=0.748^{+0.108}_{-0.009}$, $\Omega_{\mathrm{m0}}=0.276^{+0.017}_{-0.016}$,
and for model with interaction ($c=0.692^{+0.135}_{-0.107}$,
$\Omega_{\mathrm{m0}}=0.281^{+0.017}_{-0.017}$ ,$\alpha=-0.006
^{+0.021}_{-0.024}$, where $\alpha$ is an interacting parameter). As these
models have more parameters than the $\Lambda$CDM model, we use the Bayesian
evidence as a model selection criterion to make comparison. We found that the
holographic dark energy models are mildly favored by the observations compared
with the $\mathrm{\Lambda CDM}$ model.
