Lithium (Li) is one of the most important light elements that was primordially synthesized in the Big Bang Nucleosynthesis (BBN). It is also an element that confused astrophysicists for decades, as its observed abundance often contradicts with the theoretical prediction in many different types of celestial objects. Li-rich giant stars are such objects. Their atmospheres contain anomaly high Li abundance than that expected by standard stellar evolution model. Although the first Li-rich giant star was discovered almost 40 years ago, their origin is still being debated. With the launch of massive spectroscopic survey program such as the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST) survey, the extending of available asteroseismology data from space satellites such as Kepler, and the developments of data-driven techniques, breakthroughs have been archived in the field of Li-rich studies. In this paper, we review the progress that was made during the past four decades, and present our up-to-date understanding to Li-rich giant stars.