We studied the geologic history, topographic expression, and gravity signature of 29 large Venusian shield volcanoes with similar morphologies in Magellan synthetic aperture radar imagery. While they appear similar in imagery, 16 have a domical topographic expression and 13 have a central depression. Typical dimensions for the central depression are 150 km wide and 500 m deep. The central depressions are probably not calderas resulting from collapse of a shallow magma chamber but instead are the result of a corona-like sagging of a previously domical volcano. The depressions all have some later volcanic filling. All but one of the central depression volcanoes have been postdated by geologic features unrelated to the volcano, while most of the domical volcanoes are at the top of the stratigraphic column. Analysis of the gravity signatures in the spatial and spectral domains shows a strong correlation between the absence of postdating features and the presence of dynamic support by an underlying plume. We infer that the formation of the central depressions occurred as a result of cessation of dynamic support. However, there are some domical volcanoes whose geologic histories and gravity signatures also indicate that they are extinct, so sagging of the central region apparently does not always occur when dynamic support is removed. We suggest that the thickness of the elastic lithosphere may be a factor in determining whether a central depression forms when dynamic support is removed, but the gravity data are of insufficient resolution to test this hypothesis with admittance methods.