MINERvA is a dedicated neutrino-nucleus cross section experiment at Fermilab in the NuMI (anti)neutrino beamline, where it was exposed to both low and medium energy configurations with a neutrino energy spectrum ranging from a few GeV to tens of GeV. The unmatched number of events in the data are complemented by a similarly large simulated sample, and their comparison allows MINERvA to probe nuclear structure and test interaction models important for neutrino oscillation experiments. Analyzers in MINERvA extract inclusive and exclusive cross sections with a comprehensive accounting of systematic uncertainty, making use of various methods of data driven background constraint, and reporting cross section data at the truth level by utilizing the D’Agostini method of iterative Bayesian unfolding. NuXTract 2023 was a workshop at CERN organized by the Neutrino Scattering Theory Experiment Collaboration (NuSTEC) towards a consensus on how to extract neutrino cross sections. MINERvA's contributions to this field and its legacy were presented and discussed at this workshop. An overview of the methods used in MINERvA cross section extraction and results, and a recap of the recent NuXTract workshop will be presented.