Geophysical methods can be used to create images of the Earth's interior that constitute snapshots at the moment of data acquisition. In many applications, it is important to measure the temporal change in the subsurface, because the change is associated with deformation, fluid flow, temperature changes, or changes in material properties. We present an overview how noninvasive geophysical methods can be used for this purpose. We focus on monitoring mechanical properties, fluid transport, and biogeochemical processes, and present case studies that illustrate the use of geophysical method for detecting timelapse changes in associated properties. The examples include: measuring uplift of the Earth's surface, compaction near a producing hydrocarbon reservoir, the seismic detection of stress changes, monitoring buildings, the detection of fluid flow along a fault zone, electrical monitoring of fluid infiltration and redox potential, and electrical and seismic monitoring of microbially mediated processes. An overlying research question in geophysical monitoring concerns the use of these time-lapse changes, notably the assesment of uncertainty, the combination of disparate data, and the interface with those who make decisions based on time-lapse information.