Everything responds to pressure, even rocks. Deformation studies involve measuring and interpreting the changes in elevations and horizontal positions of the land surface or sea floor. These studies are variously referred to as geodetic changes or ground-surface deformations and are sometimes indexed under the general heading of geodesy. Deformation studies have been particularly useful on active volcanoes and in active tectonic areas. A great amount of time and energy has been spent on measuring geodetic changes on Kilauea and Mauna Loa Volcanoes in Hawai`i. These changes include the build-up of the surface by the piling up and ponding of lava flows, the changes in the surface caused by erosion, and the uplift, subsidence, and horizontal displacements of the surface caused by internal processes acting beneath the surface. It is these latter changes that are the principal concern of this review. A complete and objective review of deformation studies on active Hawaiian volcanoes would take many volumes. Instead, we attempt to follow the evolution of the most significant observations and interpretations in a roughly chronological way. It is correct to say that this is a subjective review. We have spent years measuring and recording deformation changes on these great volcanoes and more years trying to understand what makes these changes occur. We attempt to make this a balanced as well as a subjective review; the references are also selective rather than exhaustive. Geodetic changes caused by internal geologic processes vary in magnitude from the nearly infinitesimal - one micron or less, to the very large - hundreds of meters. Their apparent causes also are varied and include changes in material properties and composition, atmospheric pressure, tidal stress, thermal stress, subsurface-fluid pressure (including magma pressure, magma intrusion, or magma removal), gravity, and tectonic stress. Deformation is measured in units of strain or displacement. For example, tilt of the ground surface on the rim of Kilauea Caldera is measured in microradians, a strain unit that gives the change in angle from some reference. The direction in which the tilt is measured must be defined - north or south, or some direction normal to the maximum changes. For displacements related to surface faulting, the changes are normally given in linear measures of offset. Changes in the diameter of a caldera can be given in either displacements or strain units. In the later case, the displacement divided by the 'original' diameter gives the strain ratio. Strains are dimensionless numbers; displacements have the dimensions of length. Vectors commonly are used to show the direction and amount of displacements in plan view. Strain results from stress. It can be elastic strain, when the strain is linearly related to stress and is recoverable; it can be viscous strain, where the rate of strain is proportional to the stress and is not recoverable; or it can be plastic strain that is often some complex stress-strain relationship, for example, elastic up to some yield strength and viscous beyond. Volcanic rocks are brittle when cold and under near-surface pressures but plastic to viscous under higher temperature and pressure regimes. It is important in deformation studies to try to define the nature of the strain and the rheology of the rocks being deformed. A good text on rheology is 'The Structure and Rheology of Complex Fluids' by R.G. Larson, 1999. Under changing tensional or compressional stresses, tiny cracks in brittle rocks may open or close, causing a quasielastic strain response. If the stresses exceed the breaking strength of the rock, brittle failure occurs, and the stress-strain relationship breaks down.