This tutorial review discusses the structural and electronic consequences of the Jahn–Teller effect in transition metal complexes, focussing on copper(II) compounds which tend to be the most studied. The nature of a Jahn–Teller distortion in molecular complexes and extended lattices can be manipulated by application of pressure or temperature, by doping a molecule into a host lattice, or simply by molecular design. Many of these results have been achieved using compounds with a trans-[CuX₄Y₂] coordination sphere, which seems to afford copper centres that are particularly sensitive to their environment. Jahn–Teller distortions lead to some unusual phenomena in molecular magnetism, and are important to the functionality of important classes of conducting and superconducting ceramics.