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Resonant x-ray scattering studies of charge order in cuprates

X-ray techniques have been used for more than a century to study the atomic and electronic structure in virtually any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional x-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom -- charge, orbital, spin, and lattice -- paved the way for the emergence and success of resonant x-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. Here we review the recent resonant x-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order -- a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant x-ray scattering, as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review will focus on the recent contributions of resonant scattering to the tremendous advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges, and discuss the future outlook for this technique.