Let $X$ be a Fano variety of lower dimension, we study its non-trivial semi- orthogonal component, called Kuznetsov components, which is widely believed to contain essential geometric information of the Fano variety itself. The numerical Grothendieck group of this category is of rank two, which can be regarded as a"noncommutative curve" I will talk about the homological, moduli theoretical, and Hodge theoretical properties of this noncommutative curve. Then I will talk about how the (birational) isomorphism class of several class of (not necessarily smooth) Fano varieties can be characterized by this category, which is known as (birational) categorical Torelli problem. If time allows, I will explain how to use this category to study hyperKahler geometry.