AbstractDensity instabilities in the lithosphere can founder gravitationally via viscous dripping and decoupling from overlying crust. The lithospheric dripping concept has been invoked across the globe, but the diversity of crustal effects, observable evidence, and tectonic settings involved in dripping remain underexplored. Here, we synthesize numerical and analogue modeling studies and geologic data from the literature, including all proposed lithospheric dripping events to‐date. We argue that two distinct styles of dripping can occur depending on crustal strength (relative to that of the mantle lithosphere). Near‐surface contraction and subsidence of strong crusts contrasts with near‐surface extension and uplift of weak crusts. We discuss these events in terms of tectonic setting, timing, size, and the main types of data associated with each event. We also find that lithospheric dripping is associated with a distinct suite of geological observations including sedimentological, structural, volcanic, and geophysical data, which can be used to distinguish strong crusts from weak crusts. We find 27 events for which lithospheric dripping is a key hypothesis, including 9 with clear evidence for strong‐crust dripping and 3 with clear evidence of weak‐crust dripping. We review emerging research methods have the potential to detect the signals of dripping in the geologic and geophysical record, and we suggest additional techniques in light of our strong‐crust versus weak‐crust framework. The diverse tectonic settings and inferred consequences of these lithospheric drips, if confirmed, would demand a shift in our understanding of continental geology to emphasize the role of vertical removal of continental lithosphere.