  Bow-shock pulsar wind nebulae (PWNe) show a variety of morphological shapes.
We attribute this diversity to the geometrical factors: relative orientations
of the pulsar rotation axis, proper velocity, and the line of sight (magnetic
inclination angle may also have a certain influence on the morphology). We
identify three basic types of bow-shock nebulae: (i) a "Rifle Bullet" (pulsar
spin axis and proper velocity are aligned); (ii) a "Frisbee" (pulsar spin axis
and proper velocity are orthogonal with the spin axis lying in the plane of the
sky), and (iii) a Cart Wheel" (like frisbee but the spin axis is perpendicular
to the plane of the sky). Using 3D RMHD simulations, as well as analytical
calculations, we reproduce the key morphological features of the bow-shock
PWNe, as well as variations, are seen across different systems. magnetic
stresses within the shocked pulsar wind affect the overall structure strongly,
producing "whiskers", "tails", "filled-in" and "mushroom" shapes, as well as
non-symmetric morphologies. On the other hand, the interstellar medium
inhomogeneities and the anisotropy of the energy flux in the pulsar wind have
only a mild impact of the PWN morphology. In a few cases, when we clearly
identify specific morphological structures, our results do not favor alignment
of the pulsar spin axis and proper velocity. Our calculations of the underlying
emission processes explain the low synchrotron X-ray efficiency (in terms of
the spin-down luminosity) and imply an energetical subdominant contribution of
the inverse Compton process.
