A non-commutative view of Fano threefolds

The classification of Fano threefolds of Picard rank one gains more structure when instead of varieties, we consider a natural subcategory of its derived category, now called Kuznetsov component.
I will give an overview of recent results about, and based on, these Kuznetsov components. The methods involve moduli spaces of Bridgeland-stable objects, and equivariant categories.