This paper presents several concepts of deployable space structures with emphasis on their relation to the basic principles of mechanics on which the concepts depend. The following subjects are treated: the coilable longeron extendible mast and the theory of “Elastica” by Euler and Kirchhoff; the two-dimensionally deployable array and the theory of elastic surfaces (“Plate Elastica”) by Miura and Tanizawa; the variable geometry truss and the theory of truss by Mobius; the tension truss antenna and the theory of truss.