  We analyze the relation between teleparallelism and local Lorentz invariance.
We show that generic modifications of the teleparallel equivalent to general
relativity will not respect local Lorentz symmetry. We clarify the reasons for
this and explain why the situation is different in general relativity. We give
a prescription for constructing teleparallel equivalents for known theories. We
also explicitly consider a recently proposed class of generalized teleparallel
theories, called f(T) theories of gravity, and show why restoring local Lorentz
symmetry in such theories cannot lead to sensible dynamics, even if one gives
up teleparallelism.
