  The superspace formulation of the worldvolume action of twistor string models
is considered. It is shown that for the Berkovits-Siegel closed twistor string
such a formulation is provided by a N=4 twistor-like action of the tensionless
superstring. A similar inverse twistor transform of the open twistor string
model (Berkovits model) results in a dynamical system containing two copies of
the D=4, N=4 superspace coordinate functions, one left-moving and one
right-moving, that are glued by the boundary conditions.
  We also discuss possible candidates for a tensionful superstring action
leading to the twistor string in the tensionless limit as well as
multidimensional counterparts of twistor strings in the framework of both
`standard' superspace and superspace enlarged by tensorial coordinates
(tensorial superspaces), which constitute a natural framework for massless
higher spin theories.
