  The notion of spacetime symmetry is essential to describe gravitating
physical systems like planets, stars, black holes, or the universe as a whole,
since they possess, at least to good approximation, spherical, axial, or
spatially homogeneous and isotropic symmetry, respectively. This article gives
a quick overview over the known facts on spacetime symmetries in teleparallel
gravity. The most general spherical, axial, or spatially homogeneous and
isotropic tetrads in Weitzenb\"ck gauge are presented and a brief discussion
about symmetric solutions of the anti-symmetric field equations in
$f(T,B,\phi,X)$-gravity is given.
