In this talk, we will discuss the calculation of the full x-dependence of collinear PDFs in the framework of Lattice QCD, using the so-called quasi-distribution approach. This method was introduced by Xiangdong Ji in 2013 and intensively developed thereafter. We will present the computation by the Extended Twisted Mass Collaboration, employing twisted mass fermions with light quark mass set to its physical value. The relevant matrix elements obtained on the lattice were non-perturbatively renormalized and converted to the MSbar scheme. A matching process was applied together with nucleon mass corrections, leading to the reconstruction of light-cone PDFs. We observe a similar behavior between the lattice and phenomenological data, and for both types of polarized PDFs a nice overlap for a range of Bjorken-x values. This presents a major success for the emerging field of direct calculations of parton distributions using Lattice QCD. We will also present exploratory results from our on-going computation of GPDs using Ji's method. Prospects of the field will be discussed, along with a very brief review of other approaches to access the x-dependence of PDFs and other partonic functions.