  This brief review discusses the existence conditions of wormhole throats and
wormholes as global configurations in general relativity under the assumptions
of cylindrical and axial symmetries. It is pointed out, in particular, that
wormhole throats can exist in static, cylindrically symmetric space-times under
slightly different conditions as compared with spherical symmetry. In
cylindrical space-time with rotation, throats can exist in the presence of
ordinary matter or even in vacuum; however, there are substantial difficulties
in obtaining asymptotically flat wormhole configurations without exotic matter:
such examples are yet to be found. Some features of interest are discussed in
static, axially symmetric configurations, including wormholes with singular
rings and wrongly seeming regular wormhole throats in the Zipoy-Voorhees vacuum
space-time.
