We present the first complete parametrization for the matrix elements of the generic light-front gauge-invariant energy-momentum tensor, derive the expressions giving separately the spin and orbital angular momentum of quarks and gluons as probed in high-energy scattering experiments, and discuss the relations with two-parton generalized and transverse-momentum dependent distributions. As a by-product, we recovered the Burkardt sum rule, clarified its physical meaning and obtained similar new sum rules for higher-twist distributions.