We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from a global analysis of the available hard scattering data and superseding the MMHT14 sets. The parameterisation is now adapted and extended and we include a large number of new data sets: the final HERA and Tevatron data, and a significant number of LHC data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit. There are some changes to central PDF values and a significant reduction in the uncertainties, but the PDFs and the predictions using them are generally within one standard deviation of the MMHT14 results. We discuss the phenomenological impact of our results.