Lateral inhomogeneity in biological membranes has been linked with many cellular functionalities including protein sorting and signal transduction. Fluid phase coexistence has been extensively studied by modelling membranes as bulk mesophases and as giant unilamellar vesicles (GUVs). However, the basis for microdomain formation in cells remains uncertain, and this is thought to be due to the small domain size and the highly dynamic nature of the cell membrane. The application of high pressure technology offers an ideal biophysical tool for the study of phase behaviour in model membranes both in and out of equilibrium. By coupling high-pressure technology with fluorescence microscopy we have been able to simultaneously induce and visualize phase separation in GUVs. This allows the structural dynamics (including domain size and morphology in individual vesicles) to be studied, which ideally compliments small angle x-ray scattering (SAXS) measurements of bulk mesophase properties. We employ high pressure technology to induce thickness mismatch and therefore alter the line tension between coexisting liquid domains, and to study the pressure effects on the lateral structuring of membranes containing general anaesthetics. The ability to trigger rapid phase separation using pressure-jumps across the phase boundary has been used to study the dynamic evolution of structural changes, with time-resolved microscopy and SAXS giving an insight into transition kinetics, energetics and mechanisms.