Collisions between nuclei at ultrarelativistic energies produce a colour-deconfined plasma that expands explosively and rapidly reverts to the colour-confined (hadronic) state. In non-central collisions, the zone of hot matter is transversely anisotropic and may be 'tilted' relative to the direction of the incoming beams. As the matter cools and expands into the vacuum, the evolution of the system shape depends sensitively on the dynamical response of the plasma under extreme conditions. Two-pion intensity interferometry performed relative to the impact parameter can be used to measure the approximate final shape of the system when pions decouple from the system. We use several transport models to illustrate the dependence of the final shape on the QCD equation of state and late-stage hadronic rescattering. The dependence of the final shape on collision energy may reveal non-trivial structures in the QCD phase diagram. Indeed, the few measurements published to date show an intriguing behaviour in an energy region under intense experimental and theoretical scrutiny, as signatures of a first-order phase transition may appear there. We discuss strong parallels between shape studies in heavy-ion collisions and those in two other strongly coupled systems.