  This a brief review on $F(T)$ gravity and its relation with k-essence.
Modified teleparallel gravity theory with the torsion scalar has recently
gained a lot of attention as a possible explanation of dark energy. We perform
a thorough reconstruction analysis on the so-called $F(T)$ models, where $F(T)$
is some general function of the torsion term, and deduce the required
conditions for the equivalence between of $F(T)$ models with pure kinetic
k-essence models. We present a new class of models of $F(T)$-gravity and
k-essence.
