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Abstract Historically, seismic migration has been the practice (science, technology, and craft) of collapsing diffraction events on unmigrated records to points, thereby moving (“migrating”) reflection events to their proper locations, creating a true image of structures within the earth. Over the years, the scope of migration has broadened. What began as a structural imaging tool is evolving into a tool for velocity estimation and attribute analysis, making detailed use of the amplitude and phase information in the migrated image. With its expanded scope, migration has moved from the final step of the seismic acquisition and processing flow to a more central one, with links to both the processes preceding and following it. In this paper, we describe the mechanics of migration (the algorithms) as well as some of the problems related to it, such as algorithmic accuracy and efficiency, and velocity estimation. We also describe its relationship with other processes, such as seismic modeling. Our approach is tutorial; we avoid presenting the finest details of either the migration algorithms themselves or the problems to which migration is applied. Rather, we focus on presenting the problems themselves, in the hope that most geophysicists will be able to gain an appreciation of where this imaging method fits in the larger problem of searching for hydrocarbons.