Published online by Cambridge University Press: 25 May 2016
Lithium continues to be a surprising element and more than ever the study of its creation, destruction and distribution is giving us tools to understand, not only the chemical evolution of this element, but also the nature of mass loss of evolved giants and nucleosynthesis of other elements in cases of very low-metal giants. It also helps to set constraints for cosmological models. The presence of very strong lithium lines in some giant stars of different spectral types and stages of evolution has been considered up to the end of the nineties as a puzzle. To solve this problem, non standard evolutionary mechanisms must be invoked. We review here all the mechanisms presented in the literature and which are divided into internal and external processes of lithium enrichment. We will also discuss the observational tests which are being performed in order to discard (or not) some of them. In any case, the more realistic values of the lithium abundances in giants are, as we will see, the main test of these proposed scenarios. Because of this importance we discuss here the state of art of the Non-LTE determinations of lithium abundances in strong lithium giants. Evolved giants, with lithium abundances larger than that of the interstellar medium and with their important mass losses can be considered the most realistic sources of lithium in the Galaxy. We believe that a complete physical picture of this problem will give a powerful tool to understand the chemical evolution of a large part of all light elements.