It has been suggested that impacts of comets or asteroids on the surface of the Earth can cause polarity reversals of the geomagnetic field and flood basalts. Several models that have been proposed to explain this link between external and internal geologic processes are critically evaluated in light of our current knowledge of the structure and dynamics of the mantle and core. Proposals by Pal and Creer, Muller and Morris, and Burek and Wänke that impacts can induce reversals of the geomagnetic field, are each found to require the action of several unsubstantiated novel processes. In particular, the Muller-Morris proposal requires a novel and unspecified mechanism for rapid buildup of polar ice. The dynamic coupling between core and mantle is shown to be too strong to allow the large angular displacements required by their model. Proposals by Rampino and Stothers and Alt and others that impacts can trigger prompt flood basalts are found to be dynamically untenable. It is concluded that no viable model has yet been proposed to link impacts with reversals or flood-basalt volcanism.