Tensegrity structures can be defined as structural mechanisms having separate tension and compression members, where compression members are discontinuous and float in a network of tension members. Before incorporating tensegrity into major construction works, stability and safety of tensegrity as a structure has to be studied and scrutinized properly. Being a recent design philosophy, there are not many elaborate literature reviews available on tensegrity structures pertaining to the field of civil engineering. This paper aims to bring together most of the research works done in design as well as health monitoring of tensegrity structures. So far, they have found practical application in stadium roofs, domes and bridges having demand of large column-free spaces. The studies relevant to design procedures involving form finding, structural stability and load analysis have been discussed. Very few researches, focusing on health monitoring of tensegrities, are available, which have also been discussed, thereafter highlighting the need of more research work in this field.