Abstract: The abundance of Lithium constrains models of big bang nucleosynthesis, stellar structure and the age of stellar clusters. Lithium abundances therefore play a special role in our understanding of the universe. However, there are two major outstanding puzzles about stellar lithium abundances. Population II dwarfs are observed to possess lithium abundances in a plateau which is lower than the primordial value by a factor of three, and no stars are detected in the forbidden zone". Where does the lithium go to? In red giant branch stars, lithium should be burnt because of their deep convective envelope, bu about 1% of red giant stars exhibit glaring exceptions. Some of them even display lithium abundances even higher than the primordial value. These stars cannot be explained by standard stellar evolution models. Where does the lithium come from? I will talk about these two puzzles and possible solutions from both theoretical and observational perspectives.