This paper explores the possibilities of transformable structures in architectural and structural engineering. Key aspects concerning the design, analysis and construction of mobile, as well as adaptable constructions, are explained. The transformation of such structures, intended to meet changing require¬ments, is done by using mechanisms (deployable/foldable) or reconfig¬urable components (demountable kit-of-parts). Transformable structures can adapt their shape or function according to changing circumstances (Fig. 1 & 2), to meet rapidly evolving needs, induced by a society which - progressively - embraces the concept of sustainable design. This is further supported by the understanding that structures are not designed in an end state, but in a transition state, hence 'transformable structures'. Based on how this transformation is realised, two groups of structures can be distinguished. The transformation of the structure is primarily done by either: (i) incorporating a kinematic mechanism, enabling the structure to deploy from a compact configuration (e.g. for transport) to a larger, expanded state in which it can fulfil its architectural function (e.g. providing shelter) or, (ii) by designing and realising the structure as a kit-of-parts system (cfr. Meccano construction toy) with dry, reversible connections between the constitutive components, enabling design for disassembly, whereby all components can be reconfigured, replaced or re-used. The former systems are primarily aimed at the field of temporary construction, in which lightweight, deployable structures are of great use, while the latter are primarily aimed at allowing a structure to be adapted gradually over time. The paper explores the possibilities and limits of both systems, including topics such as geometric design, kinematic behaviour, structural analysis, design- and analysis software and sustainable design. Conclusions are drawn on the current state-of-the-art and suggestions are made for future research. This paper servesas an introduction to the other papers participating in the special session on 'Transformable Structures' at the HPSM 2012 Conference.