Parton distribution functions (PDFs) provide a description of the quark and gluon content of the proton. They are important input into theoretical calculations of hadronic observables, and are obtained by fitting to a wide range of experimental data. The NNPDF approach to fitting PDFs provides a robust and reliable determination of their central values and uncertainties. The PDFs are modelled using neural networks, while the uncertainties are generated through the use of Monte Carlo replica datasets. In this thesis I provide an in depth description of development of the latest NNPDF determination: NNPDF3.0. A number of novel adaptations to the genetic algorithm and network structure are outlined and the results of tests as to their effectiveness are shown. Centrally, the use of closure tests, where artificial data is generated according to a known theory and used to perform a fit, has been instrumental in both the development and validation of the NNPDF3.0 approach. The results of these tests, which demonstrate the ability of our methodology to reproduce a known underlying law, are investigated in detail. Finally, results from the NNPDF3.0 PDF sets are presented. The parton distributions obtained are compared with results from other PDF collaborations, and PDFs fit to limited datasets are also discussed. Physical observables relevant for future collider runs are presented and compared to other determinations.