Deviations from unitarity of the CKM matrix in the quark sector are considered excellent windows to probe physics beyond the Standard Model. In its leptonic counterpart, the PMNS matrix, these searches are particularly motivated, as the new physics needed to generate neutrino masses often leads to non-unitary mixing among the standard neutrinos. It is then interesting to consider how neutrino oscillations are affected in such scenario. This simple question is, however, subject to several subtleties: What is the correct way to define oscillation probabilities for a non-unitary mixing matrix? Do these probabilities add up to one? Does a non-unitary mixing matrix lead to observable flavor transitions at zero distance? What is the interplay between unitarity constraints obtained from neutrino oscillations and from electroweak precision data? This work aims to shed light on these issues and to clarify the corresponding misconceptions commonly found in the literature. We also compile updated bounds from neutrino oscillation searches to compare with those from flavour and electroweak precision observables.