Abstract: We first announce our recent result on adjunction and inversion of adjunction.Then we clarify the relationship between our inversion of adjunction and Hacon's inversion of adjunction for log canonical centers of arbitrary codimension.Key words: Adjunction; inversion of adjunction; minimal model program.1. Introduction.In [9], we established the following adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.Theorem 1.1 (Adjunction and Inversion of Adjunction, see [9]).Let X be a normal variety and let Á be an effective R-divisor on X such thatLet W be a log canonical center of ðX; ÁÞ and let : Z !W be the normalization of W . Then there exist a b-potentially nef R-b-divisor M and an R-b-divisor B on Z such that B Z is effective with