  The strong force which binds hadrons is described by the theory of Quantum
Chromodynamics (QCD). Determining the character and manifestations of QCD is
one of the most important and challenging outstanding issues necessary for a
comprehensive understanding of the structure of hadrons. Within the context of
the QCD parton picture, the Parton Distribution Functions (PDFs) have been
remarkably successful in describing a wide variety of processes. However, these
PDFs have generally been confined to the description of collinear partons
within the hadron. New experiments and facilities provide the opportunity to
additionally explore the transverse structure of hadrons which is described by
Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent
Parton Distribution Functions (TMD PDFs). In our previous review, we compared
and contrasted the two main approaches used to determine the collinear PDFs:
the first based on perturbative QCD factorization theorems, and the second
based on lattice QCD calculations. In the present report, we provide an update
of recent progress on the collinear PDFs, and also expand the scope to
encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state
of the various calculations, and consider what new data might be available in
the near future. We also examine how a shared effort can foster dialog between
the PDF and Lattice QCD communities, and yield improvements for these
generalized PDFs.
