“Push-and-pull”efficient structures have been inconceivable between XVIII centuries.It is because of the incapacity of obtain an efficient behaviour of tensioned material.Since XVIII centuries,architecture developed some structural knowledge generating novel structural forms in the architecture and engineering that were not known before.Tensegrities and tensioned structures were studied due to the knowledge of geometry and tension.Some investigations about tensegrities and tensioned structures have been developed since that moment.Tensegrities are bar and cable structures that work only in compression or tension efforts.Bars and cables are balanced,but in appearance the growth is disorderly.Most of deployable structures are based on tensegrity systems.The research is focused in presenting a summary of tensegrities and tensioned architectures that have been used in the structural design of novel patterns.The research of adequate materials to tension efforts will be crucial in this study.The investigation presents an important state of the art that provides technical solutions to apply on novel architectures based on tensegrities and tensioned structures.The research is useful to produce the current constructive solutions based on these constructive systems.