Tensegrity system is a relatively new structural system suitable for the design of light and adaptable structures which create the impression of a bunch of rods floating in the air. These structural systems are known under various names depending on a particular approach: integrally strained systems, self-stabilizing systems, self-straining networks, critical and overcritical network systems. The structural function of such systems results from linking their constituent elements by means of tensile forces into an integral whole. This principle lies behind their name tensegrity (tensional integrity). One of the main objectives in the design of wide span structural systems is to reduce their own weight as much as possible. Therefore ingenious structural systems have been invented. Their reduced weight results from a reduced number of rods in compression. Thus the stability of the system is achieved by introducing self-balancing strain created by cables (elements in tension) and rods (elements in compression). These systems can therefore be defined as systems whose rigidity results from a self-straining balanced state between tensile cables and compressive elements independently of any outside activity. Self-straining that is responsible for their rigidity is independent of any devices that usually help to achieve a balanced state of straining. The geometric form of the spatial system is created by a periodic combination of basic modules whose integral parts are cables and rods. Some forms of tensegrity structures are reminiscent of the already familiar structures, trusses and beam-and-stringer grids but with a different flow of forces and spatial stability. The originality of tensegrity structures lies in its complex geometry and structural function resulting in a specific mechanic behaviour differing from the conventional spatial systems. Three historical figures are usually considered as the inventors of tensegrity structures: R. Buckminster Fuller, David Georges Emmerich and Kenneth D. Snelson. Fuller's work has stimulated many researchers who have been exploring this field and searching for practical application of these systems. The first attempts at constructing tent-like structures in the 19605 (Frei Otto) were followed by a period (19705) in which strained structures gained popularity especially after the Olympic stadium in Munich had been built up. Numerous research projects have contributed substantially to eliminate the obstacles to practical application of tensegrity structures. Researches focused on multi-disciplinary aspect of the issue have resulted in an adjustable technology for design and analysis of integrally strained structures and have developed successful design innovations applicable to tensegrity structures. Despite the fact that tensegrity structures have for a long time been avoided and unjustly neglected within the fields of architecture and structural engineering, they have recently, however, become an accepted structural form. Advanced technology and a developing theory of integrally strained structures have helped to eliminate prejudices about these forms of structures. Finding an initial form that is stable even when stressed has certainly speeded up the evolution from sculpture to structure. Modeling is mainly based on three different approaches: by displacement, by forces and by energy. The mathematical tools necessary for the analysis of rigidity and stability of tensegrity structures is extremely complex since an appropriate modeling requires mastery and control of the following: the position of a tensegrity structure in multi-dimensional space, rigidity and straining matrices, the concepts of self-straining and proper straining, the balance and disassembly of forces. The examples of the already built tensegrity structures range from domes, towers, roof and arch structures, tents, pavilions, and bridges to artistic and everyday objects (furniture). It is certain that researches on tensegrity structures will continue into the future. The examples shown here confirm their applicability when covering large spans, bridges with short spans or as supports of lightweight infrastructural systems. Although further and more thorough researches are needed, it is quite clear that a deeply rooted assumption about the inapplicability of tensegrity structures is nowadays successfully refuted. However, successful application of new technologies to tensegrity structures requires close cooperation between architects and structural engineers as an essential prerequisite for future creative and innovative solutions.