This review is focused on neutrino mixing and neutrino oscillations in the light of the recent experimental developments. After discussing possible types of neutrino mixing for Dirac and Majorana neutrinos and considering in detail the phenomenology of neutrino oscillations in vacuum and matter, we review all existing evidence and indications in favour of neutrino oscillations that have been obtained in the atmospheric, solar and LSND experiments. We present the results of the analyses of the neutrino oscillation data in the framework of mixing of three and four massive neutrinos and investigate possibilities to test the different neutrino mass and mixing schemes obtained in this way. We also discuss briefly future neutrino oscillation experiments.

We discuss a neutrino mass matrix M ν originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle θ 13 of the lepton mixing matrix U is allowed and-in the usual phase convention-CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a seesaw extension of the Standard Model, with three right-handed neutrinos and three Higgs doublets, where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard CP symmetry.

We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while θ 13 = 0 and the solar mixing angle θ 12 remains undetermined; without finetuning, θ 12 will be large but non-maximal. Our extension of the Standard Model has three right-handed neutrino singlets ν R and implements the seesaw mechanism. Furthermore, we have an enlarged scalar sector with three Higgs doublets and two scalar gauge singlets; the latter have masses and vacuum expectation values of the order of the seesaw scale. Lepton mixing stems exclusively from the ν R Majorana mass matrix, where non-diagonal elements are generated by the vacuum expectation values of the scalar singlets. The model predicts a neutrino mass spectrum with m 3 > m 2 > m 1 , and the effective Majorana mass of neutrinoless ββ decay is equal to m 1 m 2 /m 3

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We study the conditions for neutrino oscillations in a field-theoretical approach by taking into account that only the neutrino production and detection processes, which are localized in space around the coordinates x ជ P and x ជ D , respectively, can be manipulated. In this sense the neutrinos whose oscillations are investigated appear as virtual lines connecting production with detection in the total Feynman graph and all neutrino fields or states to be found in the discussion are mass eigenfields or eigenstates. We perform a thorough examination of the integral over the spatial components of the inner neutrino momentum and show that in the asymptotic limit Lϭ͉x ជ D Ϫx ជ P ͉→ϱ the virtual neutrinos become ''real'' and under certain conditions the usual picture of neutrino oscillations emerges without ambiguities.