In this talk we reexamine the possibility of evaluating parton distribution functions from lattice simulations. We show that, while in principle individual moments can be extracted from lattice data, in all cases the process of renormalization, hindered by lattice momenta limitation, represents an obstruction to a direct calculation of the full parton distribution function from QCD simulations. We discuss the case of the Ji quasi-parton distribution functions, the possibility of using the reduced Ioffe-time distributions and the more recent proposal of directly subtracting power divergent mixings in perturbation theory.