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We survey recent results on the existence of K\"ahler-Einstein metrics oncertain smoothable Fano varieties, focusing on the importance of such metricsin the construction of compact algebraic moduli spaces of K-polystable Fanovarieties. Moreover, we give some applications and we discuss some naturalproblems which deserve future investigations.

K\"ahler-Einstein metrics on Q-smoothable Fano varieties, their moduli and some applications