In this lecture, I will talk about my recent work which is still in progress on optimal destabilization of K-unstable Fano varieties  joint with Harold Blum and Yuchen Liu. K-unstable Fano varieties are those with $\delta$-invariants strictly smaller than one. Optimal destabilization means a degeneration of the given Fano variety whose central fiber preserves $\delta$-invariant. I will introduce a theory we have developed to study K-unstable Fano varieties. As an application, I will prove some approximation results for $\delta$-invariant.