Coronal mass ejections (CMEs) are a major transient input of mass and energy into the solar wind. We review some of the past and present concepts that influence the development of models of coronal mass ejections, both for CME initiation and CME evolution and propagation in the solar wind. We use the flux cancellation model to illustrate present research on CMEs. Primarily for convenience, modeling of CME propagation has usually been treated separately from the initiation problem. We suggest that future computational modeling of interplanetary CMEs is likely to emphasize the need to study coronal initiation and solar wind propagation together. © 2003 American Institute of Physics