Lipids, which provide valuable model systems for membranes, display a variety of polymorphic phases, depending on their molecular structure and environmental conditions. By use of x-ray and neutron diffraction, infrared spectroscopy and calorimetry, the temperature and pressure dependent structure and phase behaviour of several lipid systems, differing in chain configuration and headgroup structure, have been studied. Besides lamellar phases also nonlamellar phases, such as the inverted hexagonal H-II phase and bicontinuous cubic phases, have been investigated. Hydrostatic pressure has been used as a physical parameter for studying the stability and energetics of lyotropic mesophases, but also because high pressure is an important feature of certain natural membrane environments (e.g., marine biotopes) and because the high-pressure phase behaviour of biomolecules is of biotechnological interest. Neutron scattering in combination with the H/D contrast variation technique has been used to the study of lateral organization of phase-separated binary lipid mixtures with distinct mixing properties. Within their two-phase coexistence regions large-scale concentration fluctuations appear, and the morphology of these fluctuations can be characterized as a complex heterogeneous system of coexisting clusters having fractal-like properties. By using the pressure-jump relaxation technique in combination with time-resolved synchrotron x-ray diffraction, the kinetics of different lipid phase transformations were also investigated. The time constants for completion of the transitions are dependent on the direction of the transition, the symmetry and topology of the structures involved, and also on the pressure-jump amplitude. In several cases also intermediate structures can be detected under non-equilibrium conditions.