  The f(T) gravity is nowadays being widely used for cosmological model
building, as well as for constructing spherically symmetric solutions. In its
classical pure tetrad formulation it violates the local Lorentz symmetry in the
space of tetrads. By using an appropriate spin connection it can be brought to
a formally Lorentz invariant shape. However, despite some mathematical elegance
obtained and new options of looking for non-standard couplings to matter
probably made possible, it is fully equivalent in itself to the initial
formulation. It seems that this fact, that the covariantisation does not in
principle change anything, is not understood well by the community. Therefore
we give a pedagogical introduction to these topics. And, on top of that, we
show that obtaining the explicit equations for spherically symmetric solutions
in f(T) gravity is not very difficult computationally and can be easily done
even without any computer at hand.
