Deployable structures have the capacity to transform and predictably adopt multiple predetermined configurations, moving through known paths, while deploying in a controlled and safe way. These characteristics introduce benefits when considering issues such as ease of transportation, erection and the overall sustainability of the structure by means of high material efficiency, modularisation and maximum use of natural energy resources. The aim of this article is to provide a critical review of existing attempts at classifying deployable structures identifying connections between different families through their mechanical and structural behaviours. The classifications selected consider theoretical and applied deployable structures, not focusing on a single application of deployable structures but including those ranging from spatial applications, to temporary and disaster relief structure, through to medical applications, providing coherence where terminology varies between applications. In order to gain a consistent understanding, tree diagrams were created for the review/classification to allow drawing commonalities and establishing differences between authors. A chronological approach was adopted, using key review work as focal points for the timeline, complemented by smaller more specific pieces of work. This enabled the identification of common features and divergences between the different authors, bringing to the conclusion that a clear, comprehensive, consistent and unified classification of deployable structures is currently missing within the field.