Allusion, or alluding, is a figure of speech that makes a reference to someone or something by name (a person, object, location, etc.) without explaining how it relates to the given context, so that the audience must realize the connection in their own minds. When a connection is directly and explicitly explained (as opposed to indirectly implied), it is instead often simply termed a reference. In the arts, a literary allusion puts the alluded text in a new context under which it assumes new meanings and denotations. Literary allusion is closely related to parody and pastiche, which are also "text-linking" literary devices.

In a wider, more informal context, an allusion is a passing or casually short statement indicating broader meaning. It is an incidental mention of something, either directly or by implication, such as "In the stock market, he met his Waterloo."

In the most traditional sense, allusion is a literary term, though the word has also come to encompass indirect references to any source, including allusions in film or the visual arts. In literature, allusions are used to link concepts that the reader already has knowledge of, with concepts discussed in the story. It is not possible to predetermine the nature of all the new meanings and inter-textual patterns that an allusion will generate. In the field of film criticism, a filmmaker's intentionally unspoken visual reference to another film is also called an homage. It may even be sensed that real events have allusive overtones, when a previous event is inescapably recalled by a current one. "Allusion is bound up with a vital and perennial topic in literary theory, the place of authorial intention in interpretation", William Irwin observed, in asking "What is an allusion?"

Without the hearer or reader comprehending the author's intention, an allusion becomes merely a decorative device. Allusion is an economical device, a figure of speech that uses a relatively short space to draw upon the ready stock of ideas, cultural memes or emotion already associated with a topic. Thus, an allusion is understandable only to those with prior knowledge of the covert reference in question, a mark of their cultural literacy.

The origin of allusion is from the Latin noun allusionem "a playing with, a reference to", from alludere "to play, jest, make fun of", a compound of ad "to" + ludere "to play". Recognizing the point of allusion's condensed riddle also reinforces cultural solidarity between the maker of the allusion and the hearer: their shared familiarity with allusion bonds them. Ted Cohen finds such a "cultivation of intimacy" to be an essential element of many jokes. Some aspect of the referent must be invoked and identified for the tacit association to be made; the allusion is indirect in part because "it depends on something more than mere substitution of a referent".

The allusion depends as well on the author's intent; a reader may search out parallels to a figure of speech or a passage, of which the author was unaware, and offer them as unconscious allusions—coincidences that a critic might not find illuminating.^{[dubious – discuss]} Addressing such issues is an aspect of hermeneutics.

William Irwin remarks that allusion moves in only one direction: "If A alludes to B, then B does not allude to A. The Bible does not allude to Shakespeare, though Shakespeare may allude to the Bible." Irwin appends a note: "Only a divine author, outside of time, would seem capable of alluding to a later text." This is the basis for Christian readings of Old Testament prophecy, which asserts that passages are to be read as allusions to future events.

Allusion differs from the similar term intertextuality in that it is an intentional effort on the author's part. The success of an allusion depends in part on at least some of its audience "getting" it. Allusions may be made increasingly obscure, until at last they are understood by the author alone, who thereby retreats into a private language.