Lightweight structures are essential in a range of industries and applications. For example, in the aerospace industry the need to minimise structural mass in order to reduce fuel burn and hence cost and emissions is a continuous driver in meeting the needs of both customers and legislative requirements. This leads to the design of a range of slender, lightweight structures comprising stiffened plates and shells which can become unstable under loadings which involve a compressive component. The consequent local or global buckling can cause catastrophic failure, and must be fully understood in order to use such structures in optimised designs. Manufacturing slender structures from materials such as fibre composites and fibre metal laminates with attractive specific properties provides further potential to reduce weight, and also the opportunity to tailor the material by using optimised lay-ups to meet the required load cases. This tailoring can be further explored in the design of structures capable of morphing to improve structural or even aerodynamic performance. However the added complexity introduced by using these materials must also be considered. In cases where initial buckling is localised and results in a stable postbuckling path which can provide additional load carrying capacity, the design becomes limited by material failure and this must also be incorporated into any models developed to understand the behaviour of the structure. Finally the effects of imperfections and damage originating either from the manufacturing process or events occurring during operation must be understood.