MLA’s official site allowing singular they, and explaining how to use it.
APA's Official site allowing and endorsing singular they. It also gives usage examples and gender-inclusive alternatives.
Chicago Manual of Style's approval of singular they and explanation of grammar (e.g. “themself”).
A compilation of the history of the singular they as well as what the style guides APA, MLA, and Chicago Manual of Style recommend.
Online Writing Lab (OWL) at Purdue University’s explanation as to why singular they should be included, along with additional information on pronouns. Additional sources are linked at the bottom of the page.