In this paper, we give an overview of our studies by static and time-resolved X-ray diffraction of inverse cubic phases and phase transitions in lipids. In §1, we briefly discuss the lyotropic phase behaviour of lipids, focusing attention on non-lamellar structures, and their geometric/topological relationship to fusion processes in lipid membranes. Possible pathways for transitions between different cubic phases are also outlined. In §2, we discuss the effects of hydrostatic pressure on lipid membranes and lipid phase transitions, and describe how the parameters required to predict the pressure dependence of lipid phase transition temperatures can be conveniently measured. We review some earlier results of inverse bicontinuous cubic phases from our laboratory, showing effects such as pressure-induced formation and swelling. In §3, we describe the technique of pressure-jump synchrotron X-ray diffraction. We present results that have been obtained from the lipid system 1 : 2 dilauroylphosphatidylcholine/lauric acid for cubic–inverse hexagonal, cubic–cubic and lamellar–cubic transitions. The rate of transition was found to increase with the amplitude of the pressure-jump and with increasing temperature. Evidence for intermediate structures occurring transiently during the transitions was also obtained. In §4, we describe an IDL-based ‘AXcess’ software package being developed in our laboratory to permit batch processing and analysis of the large X-ray datasets produced by pressure-jump synchrotron experiments. In §5, we present some recent results on the fluid lamellar–Pn3m cubic phase transition of the single-chain lipid 1-monoelaidin, which we have studied both by pressure-jump and temperature-jump X-ray diffraction. Finally, in §6, we give a few indicators of future directions of this research. We anticipate that the most useful technical advance will be the development of pressure-jump apparatus on the microsecond time-scale, which will involve the use of a stack of piezoelectric pressure actuators. The pressure-jump technique is not restricted to lipid phase transitions, but can be used to study a wide range of soft matter transitions, ranging from protein unfolding and DNA unwinding and transitions, to phase transitions in thermotropic liquid crystals, surfactants and block copolymers.