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Since the discovery of neutrino oscillations, a broad experimental program has established neutrinos as massive particles with non-trivial mixing, marking the beginning of a precision era in neutrino physics. Despite this progress, several fundamental questions remain open, including the ordering of the neutrino mass spectrum, the octant of the atmospheric mixing angle, and the existence of CP violation in the lepton sector. Current and upcoming experiments using intense accelerator neutrino beams and large detectors aim to address these challenges in the near future. Beyond the standard oscillation framework, neutrinos also provide a sensitive probe of new physics. Possible non-standard properties, such as additional interactions with matter or electromagnetic effects, could modify neutrino propagation and impact oscillation measurements. In this colloquium, I will review the current status of neutrino oscillation physics, discuss future prospects for improving its precision, and comment on the robustness of the oscillation picture in the presence of physics beyond the Standard Model.