  We present a theoretical investigation of electron states hosted by magnetic
domain walls on the 3D topological insulator surface. The consideration
includes the domain walls with distinct vectorial and spatial textures. The
study is carried out on the basis of the Hamiltonian for quasi-relativistic
fermions by using a continual approach and tight-binding calculations. We
derive the spectral characteristics and spatial localization of the the
one-dimensional low-energy states appearing at the domain walls. The antiphase
domain walls are shown to generate the topologically protected chiral states
with linear dispersion, the group velocity and spin-polarization direction of
which depend on an easy axis orientation. In the case of an easy plane
anisotropy, we predict a realization of a dispersionless state, flat band in
the energy spectrum, that is spin-polarized along the surface normal.
Modification of the surface states in the multi-domain case, which is
approximated by a periodic set of domain walls, is described as well. We find
that the magnetic domain walls with complex internal texture, such as
N\'eel-like or Bloch-like walls, also host the topological states, although
their spectrum and spin structure can be changed compared with the sharp wall
case.
