Parton distribution functions (PDFs) and amplitudes (DAs) are defined near the light front frame. Within the parton model the former correspond to probability densities and the latter to wavefunctions of a given hadron. While PDFs are needed in the description of inclusive processes, DAs are important for exclusive processes like the photoproduction of pions.

Within QCD, PDFs and DAs are defined as expectation values of non-local light front operators, which complicates their evaluation in lattice QCD simulations, that are carried out in Euclidean spacetime. Recently, new methods of "directly" computing PDFs and DAs on the lattice have been suggested. I will discuss a "direct" computation of the leading twist pion DA from Euclidean Green functions in coordinate space as the easiest realization of these novel methods.

Mellin moments of DAs provide an alternative approach as these are related to expectation values of local operators, enabling their non-perturbative evaluation using "traditional" methods. Recently, for the first time, we carried out a continuum limit extrapolation of the lowest lying DAs of the octet pseudoscalar mesons and baryons across five lattice spacings. I will also present details of these studies.