  I discuss the issue of degrees of freedom in modified teleparallel gravity.
These theories do have an extra structure on top of the usual
(pseudo)Riemannian manifold, that of a flat parallel transport. This structure
is absolutely abstract and unpredictable (pure gauge) in GR-equivalent models,
however it becomes physical upon modifications. The problem is that, in the
most popular models, this local symmetry is broken but not stably so, hence the
infamous strong coupling issues. The Hamiltonian analyses become complicated
and with contradictory results. A funny point is that what we see in available
linear perturbation treatments of $f(T)$ gravity is much closer to the analysis
with less dynamical degrees of freedom which has got a well-known mistake in
it, while the more accurate work predicts much more of dynamics than what has
ever been seen up to now. I discuss possible reasons behind this puzzle, and
also argue in favour of studying the most general New GR models which are
commonly ignored due to suspicion of ghosts.
