  We investigate alternative candidates to dark energy that can explain the
current state of the universe in the framework of the generalized teleparallel
theory of gravity $f(T)$ where $T$ denotes the torsion scalar. To achieve this,
we carried out a series of reconstruction taking into account to the ordinary
and entropy-corrected versions of the holographic and new agegraphic dark
energy models. These models used as alternative to dark energy in the
literature in order describe the current state of our universe. It is remarked
that the models reconstructed indicates behaviors like phantom or quintessence
models. Furthermore, we also generated the EoS parameters associated to
entropy-corrected models and we observed a transition phase between
quintessence state and phantom state as showed by recent observational data. We
also investigated on the stability theses models and we created the $\{r-s\}$.
The behavior of certains physical parameters as speed of sound and the
Statefinder parameters are compatible with current observational data.
