Elliptical galaxies were once thought to be similar in their structure and dynamics to rotationally flattened bodies like stars. The discovery that elliptical galaxies rotate much more slowly than a fluid body with the same shape has led to a qualitative change in our understanding of the dynamics of these systems. It is now believed that elliptical galaxies are fully triaxial in shape. Self-consistent triaxial equilibria have been constructed and appear to be long-lived; they are made possible by the existence of conserved quantities, or integrals of motion, for galactic potentials without rotational symmetry. Many self-consistent equilibria are unstable; the nonexistence of elliptical galaxies with axis ratios more extreme than 3:1 is probably the result of such an instability. There is evidence for strong central mass concentrations, perhaps massive black holes, at the centers of some nearby galaxies. Recent observations suggest that many elliptical galaxies formed through the merger of two or more spiral galaxies.