Common materials have Poisson's ratio values ranging from 0.0 to 0.5. Auxetic materials exhibit negative Poisson's ratio. They expand laterally when stretched longitudinally and contract laterally when compressed. In recent years the use of textile technology to fabricate auxetic materials has attracted more and more attention. It is reflected in the extent of available research work exploring the auxetic potential of various textile structures and subsequent increase in the number of research papers published. Generally there are two approaches to producing auxetic textiles. The first one includes the use of auxetic fibers to produce an auxetic textile structure, whereas the other utilizes conventional fibres to produce a textile structure with auxetic properties. This review deals with auxetic materials in general and in the specific context of auxetic polymers, auxetic fibers, and auxetic textile structures made from conventional fibers and knitted structures with auxetic potential.