Parton Distribution Functions (PDFs) are a key element in all theoretical predictions at the LHC. The precision reached by the data and future precision prospects deeply challenge PDFs determinations. In this talk I will focus on two new frontiers. The first concerns the inclusion of theory uncertainties in PDFs. So far PDF uncertainties only reflect the experimental uncertainties of the data included in a fit. I will discuss why this is no longer an option and present a consistent approach to include them in a fit. The second frontiers concerns the interplay between PDFs and new physics, as parametrised in a SM-EFT approach. I will discuss about the often mentioned possibility of PDFs absorbing new physics and on how it is possible to assess whether this is the case or not.