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Interacting beams were first employed to determine absolute cross sections for atomic processes a half-century ago. Significant advances in many technologies have improved the precision and sensitivity of such measurements to the degree that the high quality of those early experiments seems remarkable today. Despite their early successes and continuing advances, interacting beams experiments and the determination of absolute cross sections and rate coefficients from them remain a challenge. This paper concentrates on one large-scale technical advance, the synchrotron light source that has facilitated interacting-beams measurements of cross sections for photoionization of atomic and molecular ions. Recent results will be presented for photoionization of fullerene and endofullerene molecular ions. [ABSTRACT FROM AUTHOR]