Refer, allude, advert are comparable when they mean to mention something so as to call or direct attention to it.
Refer, when unqualified, usually suggests intentional introduction and distinct mention, but often it is so qualified as to add the idea of judging to that of mentioning.
Allude, though often close to refer in the latter’s more general sense, distinctively implies indirect reference (as by a hint, a suggestive phrase, a roundabout or covert method of expression, or a figure of speech); it may suggest mere casual interest, modesty, timidity, or reticence in the one who alludes.
Sometimes, however, it connotes bias or ill will.
Advert, which basically means to turn the mind or attention to something (see ADVERT 1 ), is sometimes interchangeable with refer but in such use it may distinctively imply a slight or glancing reference interpolated in a text or utterance.