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The construction of numerous new synchrotron light sources worldwide is providing the means to study atomic and molecular photoionization processes at a level of detail that is unparalleled in even the recent past. Correspondingly, in theory, the availability of supercomputers and, perhaps more important, relatively inexpensive computer workstations, has permitted theoretical calculations to tackle more complex processes than ever before. In short, these technical developments are creating an unprecedented amount of data to be analyzed and understood.
In this volume, many of the experimental and theoretical advances of recent years will be described. We take the point of view in this introductory paper that while agreement of theory and experiment is always desirable, the main goal of researchers in this field should be to advance our understanding of the key physics governing photoionization processes in as simple a way as possible. As there can be no general prescription for achieving such a goal, we therefore present an eclectic set of examples of recent advances in experimental techniques or theoretical analysis which have achieved such simplicity in the face of complexity. For clarity, however, we review briefly beforehand some essentials of the theory of photoionization.