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Neutrino oscillation measurements provide an important window on what lies beyond the Standard Model of particle physics. These measurements may unlock the mechanism by which the universe came to become matter-dominated, and may offer hints of another mechanism to generate particles with mass. Measurements of oscillations from muon neutrinos to electron neutrinos (and their antineutrino counterpart) as a function of time provide critical inputs to understanding both mechanisms. These are challenging measurements and a variety of techniques and strategies are required to get the complete picture. This article describes the current status of our understanding of neutrino masses and how neutrinos oscillate between one flavour and another as they propagate through space and time, and what remains to be understood. Taking the next steps in this field requires a variety of approaches and a better understanding of how neutrinos interact with nuclei. This article describes two of those next steps, highlighting where Canadian groups are active, and concludes with a discussion of the broad range of additional physics that becomes accessible by having two very different large sensitive neutrino detectors making these measurements.