Higher-order processes in X-ray photoionization of atoms

There are several fourth-generation X-ray light source projects now underway around the world and it is anticipated that by the end of the decade, one or more of these X-ray free-electron lasers will be operational. In this contribution, we describe recent measurements and future plans to study both multielectron and multiphoton atomic photoionization. Although such higher-order processes are rare with present third-generation sources, they will be commonplace in experimental work with the new sources. The topics we discuss here are double K-shell ionization and two-photon X-ray photoionization.