In this talk I will present an overview of the latest efforts to constrain the structure of the proton, as encoded in the parton distribution functions (PDFs), via global PDF fits. I will focus on the MSHT global PDF fit, and on recent significant advances towards increasing precision in the QCD expansion (up to N3LO) used in the theoretical calculations entering such fits and in the corresponding inclusion of theoretical uncertainties. In addition to this progress, there are a range of important outstanding issues to resolve, notably in the impact of PDF fitting methodology and the statistical treatment of PDF uncertainties in the complex environment of a global PDF fit. I will also discuss recent attempts to address these issues, via closure testing of the MSHT PDF fits and the first like-for-like comparison with the neural network approach of NNPDF. A number of conclusions can already be drawn from this, but with much left to do in the future if true precision and accuracy in PDF determination is to be achieved.