  Following a ground-breaking proposal by Ji~\cite{PhysRevLett.110.262002},
numerical simulations of Quantum Chromo Dynamics (QCD) on a Euclidean lattice
have provided new, valuable information on the structure of hadrons. In this
talk, we briefly review the lattice approach to the reconstruction of parton
densities, highlighting the connection between lattice observables and parton
densities, with a focus on theoretical issues. Since parton distributions are
extracted from lattice data by solving an inverse problem, we discuss some of
the difficulties that affect these determinations and how they can be
formulated in a Bayesian framework.
