  We discuss the most general class of teleparallel scalar-torsion theories of
gravity in their covariant formulation. The only restrictions we impose are the
invariance of the action under diffeomorphisms and local Lorentz
transformations, as well as vanishing direct coupling of the matter fields to
the teleparallel spin connection. In this general setting we discuss the
implications of local Lorentz invariance and diffeomorphism invariance and
derive the general structure of the field equations. Further, we show how
different theories of this class are related to each other by conformal
transformations of the tetrad and redefinitions of the scalar field. We finally
show how the formalism can be generalized to an arbitrary number of scalar
fields, and provide a few examples.
