  We review the latest progress in lattice QCD calculations of the partonic
structure of hadrons. This structure is, in particular, described in terms of
$x$-dependent distributions, the simplest of which are the standard parton
distribution functions (PDFs). The lattice calculations rely on matrix elements
probing spatial correlations between partons in a boosted hadron, that can be
matched to light-cone correlations defining the relevant distributions. We
discuss the recent theoretical and practical refinements of this strategy, as
well as new exploratory directions. The latter include generalized parton
distributions (GPDs), distributions beyond leading twist, flavor-singlet
distributions and transverse-momentum dependent PDFs (TMDs). We also shortly
consider the potential future impact of lattice data on phenomenology.
