The Lithium content in stars is very sensitive to the internal stellar conditions. Indeed, Lithium is readily destroyed in the interiors of low-mass main-sequence (MS) stars and the Li in the convective envelope is progressively depleted. The Li abundance at the stellar surface was expected to be further depleted after stars leave the MS and experience the first dredge-up. However, it is now almost 40 years ago that the first (surprising) detections of Lithium-rich cool giants were reported in the literature. Lithium-rich cool giants have been mainly detected both in our Galaxy and in the Magellanic Clouds, with a few examples in other galaxies. The Li-rich cool giant stars are mainly low-mass stars near the `bump' in the red giant branch (RGB) phase or intermediate-mass stars on the asymptotic giant branch (AGB). Here I review the available spectroscopic observations of Li-rich giant stars in the Galaxy and in the Magellanic Clouds with a special emphasis on the intermediate-mass Li-rich cool giants on the AGB phase. Finally, I highlight the recent results regarding Li production on the RGB phase as obtained by on-going massive spectroscopic surveys such as Gaia-ESO, LAMOST and GALAH as well as the expected observations with future spectroscopic surveys like WEAVE and 4MOST.