Analytical modelling of structural elements susceptible to instabilities, such as thin-walled metallic components, laminated composite panels and metamaterial lattices, has recently provided fresh insights to their nonlinear behaviour. The present overview highlights some of the advantages of analytical approaches for interpreting the mechanical response of such problems in physical structures. The results from this kind of modelling, in particular for components with perfect geometries that exhibit complex instability phenomena, can provide highly valuable and in fact more generic information that can complement standard high-fidelity finite element (FE) modelling. This is because some of the necessary procedures within standard FE modelling can obscure some of the mechanical richness in the behaviour, which in turn can be readily interpreted through analytical techniques. In the present context, a series of recent studies are outlined that comprise investigations on buckling mode interaction in thin-walled metal and composite structural components, the internal buckling of mechanical metamaterials and the real-time assessment of in-situ compression members through probing and machine learning. Through these examples, the aim is to illustrate that analytical modelling still has an invaluable role to play in structural mechanics and engineering.