Singular Del Pezzo varieties

A del Pezzo variety $X$ is a Fano variety whose anticanonical class has the form $-K_X=(n-1)A$, where $A$ is an ample line bundle and $n$ is the dimension of $X$. This is a higher dimensional analog of the notion of del Pezzo surfaces. I am going to discuss biregular and birational classifications of del Pezzo varieties admitting terminal singularities.
The talk is based on a joint work with Alexander Kuznetsov.