Pressure-temperature-time (P-T-t) paths summarize the changes in pressure and temperature imposed on a metamorphic rock during orogenesis. They provide a convenient framework for the interpretation of complex metamorphic histories and also offer insight into the thermal and tectonic factors controlling metamorphism in collisional orogens. P-T-t data are acquired through a combination of textural observations, thermobarometry, and thermochronometry, and assembled into a P-T-t path using geological constraints. One-dimensional P-T-t models, assuming instantaneous deformation and thermal relaxation by conduction, are flexible and useful for testing tectonic models, particularly where geochronological constraints are available. Two-dimensional models allow more sophisticated deformation geometries and allow the effects of advection to be incorporated. Analysis of collisional orogens in terms of critical wedge theory can yield P-T-t paths that reflect coupling between thickening, uplift, exhumation, erosion, and convergence. Where rates of erosion approach rates of tectonic uplift, as is currently happening in the Southern Alps of New Zealand, high-grade metamorphic rocks can be exhumed rapidly from considerable depth. Alternatively, rapid exhumation may reflect gravity-driven extension in an over-steepened or thermally weakened orogen.