APA

Format or style, from the American Psychological Association, is commonly used for footnotes in behavioral and social science publications. APA citation is an author-year-system. It is one of the most common styles used and taught at colleges and high schools. See here for more details, including APA formatting for bibliographies.

Chicago

Format or style (also known as Turabian), created by the University of Chicago, is commonly used for footnotes in history, business, and fine arts and occasionally in the humanities, sciences, and social sciences. The Chicago style has two systems of citation. The author-date system (most common in social sciences and sciences) cites sources parenthetically in the text. The notes and bibliography system (most common in humanities) cites sources in numbered footnotes or endnotes which correspond to a superscript number in the text. See here for more details, including Chicago formatting for bibliographies.

MLA

Modern Language Association (MLA) format or style is most commonly used for footnotes in the language arts, cultural studies, liberal arts, and humanities. MLA uses short parenthetical citations within the text that are linked to an alphabetical list of work cited at the end of the document. MLA commonly cites using this format: author's last name, first name, title, publication, edition or chapter, and year. See here for more details, including MLA formatting for bibliographies.

AMA

American Medical Association (AMA) format or style is most commonly used for footnotes in medicine, biomedical research, nursing, dentistry, and other life sciences. AMA uses numerical superscript for citing sources in-text and refers to a list at the end of the work. These references appear in sequential order of when the sources were cited, instead of alphabetical order. See here for more details, including AMA formatting for bibliographies.