The phenomenon of neutrino oscillations has been established as the leading mechanism behind neutrino flavor transitions, providing solid experimental evidence that neutrinos are massive and lepton flavors are mixed. Here we review sub-leading effects in neutrino flavor transitions known as non-standard neutrino interactions (NSIs), which is currently the most explored description for effects beyond the standard paradigm of neutrino oscillations. In particular, we report on the phenomenology of NSIs and their experimental and phenomenological bounds as well as an outlook for future sensitivity and discovery reach.
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