World spinors are objects that transform w.r.t. double covering group \overline 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 \overline 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.

PACS numbers: 04.20.Gz, 03.65.Pm