Lithium (Li)-rich giants are particularly rare. According to standard stellar evolution, red giant branch stars should have very low Li abundances. Additionally, we can consider the reduced Li abundances found in the main sequence, hinting at an additional depletion there, and the extra-mixing mechanism decreasing the Li after the luminosity function bump. In this scenario, Li-enriched red giants are even more unexpected. Through asteroseismology, it has recently been identified that most of the Li-rich giants are in the core-He burning phase. Some of them, however, are still first ascending red giants. Possible explanations for this high Li abundance include an enhanced form of extra-mixing or pollution from external sources, such as planets. It has also been suggested that the high Li abundances are related to the presence of binary companions. Thus, studying different signatures in these stars would allow us to find the Li enrichment mechanism in different evolutionary phases.