The concept of cable-strut is extended from that of tensegrity. The broad interpretation of cable-strut systems includes tensegrity systems, RP (Reciprocal Prism) and CP (Crystal-cell Pyramid) system, etc. Its narrow interpretation excludes tensegrity systems. Thus this paper is divided into two parts. Part I gives concept, properties and feasibility studies of tensegrity structures to put forward cable-strut systems. Part II presents the theory and novel concepts concerning the application of cable-strut systems, and concludes that cable-strut systems are revolutionary in space structures. In this part, the essential idea of tensegrity is analyzed and the concept of tensegrity is systematically redefined. Tensegrity grids can be classified into two types of configurations: non-contiguous strut and contiguous strut. Their properties are presented and compared. The properties of the latter are also compared with those of RP grids. The low efficiency of tensegrity grids is analyzed. The feasibility studies, concerning applicable tensegrity forms and their application scale, are also introduced in this paper.