The Kuznetsov component is a very important subcategory in the derived category of coherent sheaves. In many cases, it is shown that the Kuznetsov component can control the birational geometry of Fano varieties, where the first case dates back to 2004 by Kuznetsov on cubic threefolds. After the development of a tool called stability conditions, there have been a lot of breakthroughs regarding this subcategory. Some interesting questions are raised around this topic recently, such as the geometry of the space of stability conditions on Kuznetsov components, which is known to be a complex manifold. In this talk, I will start with the definition of these notions, and give an overview of some of the latest developments in this area.