  We review recent progress in the global determination of the collinear parton
distributions (PDFs) of the proton within the NNPDF framework. This progress
includes NNPDF4.0 variants with QED effects and with missing higher order
uncertainties (MHOUs) via the theory covariance matrix formalism, as well as
PDFs based on QCD calculations at approximate N$^3$LO (aN$^3$LO) accuracy. We
present the combination of these theoretical developments resulting into
NNPDF4.0 aN$^3$LO variants accounting for QED corrections and with a photon
PDF. We compare these aN$^3$LO QED PDFs with analogous results obtained by the
MSHT group, and briefly quantify their implications at the level of
representative LHC cross-sections.
