To indicate an omitted word or phrase. To indicate a meaningful silence. [Colloq.] To indicate that a sentence has trailed off, leaving a meaningful silence.
When not to use ellipses: In place of a punctuation at the end of a complete sentence.
I keep getting Emails today in which requests or mere statements are punctuated with an ellipsis. Like, “The author is wondering about galleys. . .” “My department chair wanted to know. . . “ I can’t help reading them in a sarcastic tone, as though the writer is utterly wearied by my failure to anticipate the question (such as it is).