According to standard stellar evolution, lithium is destroyed throughout most of the evolution of low- to intermediate-mass stars. However, a number of evolved stars on the red giant branch (RGB) and the asymptotic giant branch (AGB) are known to contain a considerable amount of Li, whose origin is not always understood well. Here we present the latest development on the observational side to obtain a better understanding of Li-rich K giants (RGB), moderately Li-rich low-mass stars on the AGB, as well as very Li-rich intermediate-mass AGB stars possibly undergoing the standard hot bottom burning phase. These last ones probably also enrich the interstellar medium with freshly produced Li.