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In this article, we review recent lattice calculations on the $x$-dependenceof parton distributions, with the latter providing information on hadronstructure. These calculations are based on matrix elements of boosted hadronscoupled to non-local operators and can be related to the standard, light-conedistribution functions via an appropriate factorization formalism. There issignificant progress in several directions, including calculations of flavorsinglet parton distribution functions (PDFs), first calculations of generalizedparton distributions (GPDs), as well as the implementation of some of theapproaches for the transverse-momentum-dependent PDFs (TMD PDFs). This newdirection of lattice calculations is particularly interesting forphenomenological fits on experimental data sets, as the lattice results canhelp to improve the constraints on the distribution functions.

The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD