In the last decades, a very important breakthrough has been brought about in the elementary particle physics by the discovery of the phenomenon of the neutrino oscillations, which has shown neutrino properties beyond the Standard Model. But a full understanding of the various aspects of the neutrino oscillations is far to be achieved. In this paper the theoretical background of the neutrino oscillation phenomenon is described, referring in particular to the paradigmatic models. Then the various techniques and detectors which studied neutrinos from different sources are discussed, starting from the pioneering ones up to the detectors still in operation and to those in preparation. The physics results are finally presented adopting the same research path which has been crossed by this long saga. The problems not yet fixed in this field are discussed, together with the perspectives of their solutions in the near future. 1. Introduction Neutrino studies brought us to some of the most relevant breakthroughs in particle physics of last decades. In spite of that, the neutrino properties are still far to be completely understood. The discovery of the oscillation phenomenon produced quite a revolution in the Standard Model of elementary particles, especially through the direct evidence of a nonzero neutrino mass. The first idea of neutrino oscillations was considered by Pontecorvo in 1957 [1–3], before any experimental indication of this phenomenon. After several-decades-lasting saga of experimental and theoretical research, many questions are still open around the interpretation of this phenomenon and on the correlated aspects, on the oscillation parameters, on the neutrino masses, on the mass hierarchy, on CP violation in the leptonic sector, and on a possible existence of a fourth, sterile neutrino. The generally accepted MSW model [4–6] to interpret solar neutrino oscillations is presently validated for the oscillation in vacuum and in matter, but not yet in the vacuum-matter transition region. The shape of this transition could be influenced in a relevant way, as suggested by various theories going beyond the Standard Model as, for example, the nonstandard neutrino interactions and a possible existence of a very light sterile neutrino. For this reason, the transition region deserves further and refined experimental studies. Checks on the neutrino oscillations are under way through several experiments in data-taking phase, while few others are in preparation or even construction. These projects exploit various approaches, for example, neutrino-flavor
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