  World spinors are objects that transform w.r.t. double covering group
$\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic
mathematical results and the corresponding physical interpretation concerning
these, infinite-dimensional, spinorial representations are reviewed. The role
of groups $Diff(4,R)$, $GA(4,R)$, $GL(4,R)$, $SL(4,R)$, $SO(3,1)$ and the
corresponding covering groups is pointed out. New results on the infinite
dimensionality of spinorial representations, explicit construction of the
$\bar{SL}(4,R)$ representations in the basis of finite-dimensional non-unitary
$SL(2,C)$ representations, $SL(4,R)$ representation regrouping of tensorial and
spinorial fields of an arbitrary spin lagrangian field theory, as well as its
$SL(5,R)$ generalization in the case of infinite-component world spinor and
tensor field theories are presented.
