  The main purpose of this paper is to establish some useful partial
resolutions of singularities for pairs from the minimal model theoretic
viewpoint. We first establish the existence of log canonical modifications of
normal pairs under some suitable assumptions. It recovers Kawakita's inversion
of adjunction on log canonicity in full generality. We also discuss the
existence of semi-log canonical modifications for demi-normal pairs and
construct dlt blow-ups with several extra good properties. As applications, we
study lengths of extremal rational curves and so on.
