Theoretical progress on the formulation and classification of the quark and
gluon orbital angular momenta (OAM) is reviewed. Their relation to parton
distributions and open questions and puzzles are discussed. We give a status
report on the lattice calculation of the parton kinetic and canonical OAM and
point out several strategies to calculate the quark and gluon canonical OAM on
the lattice.Comment: 16 pages, contribution to the EPJA speical issue on "3D Structure of
the Nucleon