Demailly proves a version of the Ohsawa-- Takegoshi extension theorem which allows holomorphic sections of certain adjoint bundles on a possibly reducible and non-reduced subvariety to be extended holomorphically to the ambient complete Kähler manifold. In this talk, I will present the proof of the extension theorem of Demailly and discuss about a joint work with YoungJun Choi, which is still a work-in- progress, on applying this extension theorem to solve the (yet) conjectural dlt extension.