The x-dependence of PDFs from lattice QCD

Parton distribution functions (PDFs),  generalized PDFs (GPDs), and transverse momentum dependent PDFs (TMDs) are the fundamental objects containing all the information of the structure of hadrons as dictated by their constituents, quarks and gluons. Because they are non-perturbation quantities, we must rely on non-perturbative methods for their computation.  Although lattice QCD (LQCD) is the most successful method to access the non-perturbative physics, it is not useful in this case because PDFs are given by light-cone correlations, inaccessible to LQCD. However, several years ago Ji proposed a new method to compute PDFs in LQCD based on large momentum effective theory (LaMET). Within this method, one computes purely spatial correlations, accessible to LQCD, which can be related, upon a suitable perturbative calculation, to the light-cone correlations. In this talk, we present the state of art results for the computation of PDFs, GPDs, and TMDs using the LaMET approach, as well as discussing future directions to this field.