  We investigate modified theories of gravity in the context of teleparallel
geometries. It is well known that modified gravity models based on the torsion
scalar are not invariant under local Lorentz transformations while
modifications based on the Ricci scalar are. This motivates the study of a
model depending on the torsion scalar and the divergence of the torsion vector.
We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset
of these models and also show that this is the unique theory in this class that
is invariant under local Lorentz transformation. Furthermore one can show that
$f(T)$ gravity is the unique theory admitting second order field equations.
