Singular they is the standard English gender neutral pronoun for any individual whose gender is unknown or unspecified. For this reason, "they" pronouns are one of the three most popular pronouns used for real nonbinary people, as shown in surveys (see below). This is consistently and by far the most used pronoun among nonbinary people, with over 79% of the respondents in the 2019 Gender Census marking it as their favourite option.
Although the singular they has been used in English informally for centuries, some grammarians have questioned its use based around arguments of grammatical correctness and formality. One of the main points of contention made by grammarians is that the singular they still acts grammatically as a plural would when acting upon verbs (which they consider to be unacceptable). Despite these concerns, which became particularly prominent during and after the 19th century, the singular they is documented to have been used by Shakespeare, Jane Austen, the Oxford English Dictionary, Louis Carroll, C. S. Lewis, among others. Ever since the end of the 20th century, the singular they has been growing in both formal and informal usage to serve different purposes, and is generally in standard use today.The grammarian A. Knutson notes in his 1905 book The Gender of Words Denoting Living Beings in English, and the Different Ways of Expressing Difference in Sex the use of the singular they as a gender neutral term, pulling a quote from a magazine of the time:
The privilege of addressing the sovereign when he or she came to dine... after their coronation.Singular "they" gets a surprising number of complaints, considering people use it all the time for people whose gender is unknown. However, there are a lot of arguments that it's correct. This article on Motivated Grammar goes through a few reasons, including the fact that it's consistently been in use since Chaucer's time, around 1400. Most people are familiar with how singular "they" works, as plenty of people use it all the time without really thinking about it.
A most comprehensive article about the history of singular "they" is Henry Churchyard's web-page, Singular 'Their' in Jane Austen and Elsewhere.
Many official writing style guides and dictionaries approve the usage of singular "they" (for both "generic person" use and for writing about nonbinary people), including the MLA, the APA, and Merriam-Webster's.
The forms of "singular they" are they, them, their, theirs, themselves (themself, theirself, theirselves).
- Nominative: When I tell someone a joke they laugh.
- Accusative: When I greet a friend I hug them.
- Pronominal possessive: When someone does not get a haircut, their hair grows long.
- Predicative possessive: If I need a phone, my friend lets me borrow theirs.
- Reflexive: Each child feeds themself. Or: each child feeds theirself. Or: each child feeds theirselves. Or: each child feeds themselves. (See below for information on how this form's standard use varies by dialect.)
On Pronoun Island: http://pronoun.is/they On Pronouny: http://pronouny.xyz/pronouns/593c1223975dfa1000d4ec86
Reflexive form variants
There are several versions of the reflexive form of this pronoun: "themself," "theirself," "theirselves," and "themselves."
- Themself. The Oxford Dictionary says that "themself" has been used since the 14th century for a person of unknown sex.
- Theirself, theirselves. Dictionary.com says that "theirself" has also been used for this since about 1300. The Free Dictionary adds that "theirself" and "theirselves" are more common in southern and midland US English.
Because both "themself" and "theirself" are for talking about a single person, they're both considered non-standard or informal usage, despite the hundreds of years of common usage. The plural form of "themselves" is supposed to be more formal, but can sound strange when used for a single person, because they are not several "selves," but one "self". This is another part of the plural/singular "they" problem.
People differ about which version of the reflexive form they prefer. If someone asks to be called by "they" pronouns, it might be a good idea to ask which form of the reflexive form they prefer.
Singular they in use in fiction for nonbinary characters
- In a short sci-fi story by Benjanun Sriduangkaew, "Silent Bridge, Pale Cascade" (2013), one of the characters is described as a "neutrois," and called by "they" pronouns.
- In Kameron Hurley's fantasy novel, Empire Ascendant, all people in a consent culture get to choose which of the five gender roles they identify with. Hurley calls characters who are "ungendered" by singular they pronouns.
- In K. A. Cook's anthology Crooked Words, the character Chris asks to be called by "they" pronouns. Chris is in the short stories "Blue Paint, Chocolate and Other Similes" and "Everything In A Name."
- In Becky Chambers' novel A Psalm for the Wild-Built, the monk protagonist, Sibling Dex, is referred to with they/them pronouns. 
Singular they in use for real nonbinary people
- Some notable nonbinary people who ask to be called by "singular they" pronouns include writer Ivan E. Coyote, actor Jiz Lee, singer-songwriter Rae Spoon, rapper Raeen Roes, and singer Sam Smith.
- Deborah Rogers mentions having a trans male student who asked to be called by "they" pronouns.
- "Singular they" has been the most popular pronoun in the Gender Census, at 74% acceptance in 2015, rising to 77% in 2016, and rising again to 80% in 2017. In 2018, the pronoun fell down to 77.4%.
- Singular 'Their' in Jane Austen and Elsewhere
- Motivated Grammar: Singular they and the many reasons why it's correct
- Examples of use in Pronoun Dressing Room. You can try different variations on the pronouns, such as the variant reflexive forms, and see how they can work in sentences excerpted from classic fiction.
- Gender Census 2019 - The Full Report (Worldwide)https://gendercensus.com/post/183832246805/gender-census-2019-the-full-report-worldwide
- Henry Churchyard, "Singular 'Their' in Jane Austen and Elsewhere." http://www.crossmyt.com/hc/linghebr/austheir.html
- Knutson, A. (1905). The Gender of Words Denoting Living Beings in English, and the Different Ways of Expressing Difference in Sex. Lund: Håkan Ohlsson. pp. 3–4.
- "How do I use singular they?". The MLA Style Center. Retrieved 8 February 2021.
- "Singular "they"". APA Style. September 2019. Retrieved 8 February 2021.
- "Themself." Oxford Dictionaries. https://www.oxforddictionaries.com/us/definition/american_english/themself
- "Theirself." Dictionary.com. http://dictionary.reference.com/browse/theirself
- "Theirselves." The Free Dictionary. http://www.thefreedictionary.com/theirself
- Alex Dally MacFarlane, "Post-Binary Gender in SF: ExcitoTech and Non-Binary Pronouns." June 3, 2014. Tor. http://www.tor.com/blogs/2014/06/post-binary-gender-in-sf-excitotech-and-non-binary-pronouns
- Benjanun Sriduangkaew, "Silent Bridge, Pale Cascade." Clarkesworld Magazine. 2013. http://clarkesworldmagazine.com/sriduangkaew_12_13/
- Kameron Hurley, "Beyond He-Man and She-Ra: Writing nonbinary characters." https://intellectusspeculativus.wordpress.com/2014/09/03/guest-post-beyond-he-man-she-ra-writing-non-binary-characters-by-kameron-hurley/
- K. A. Cook, Crooked Words. Unpaged.
- Linda Codega, "An Elegy for the Rest of Us: A Psalm for the Wild-Built by Becky Chambers" https://www.tor.com/2021/07/13/book-reviews-a-psalm-for-the-wild-built-becky-chambers/
- Deborah Rogers, "'They' has arrived at the pronoun party." December 4, 2014. Times Higher Education. http://www.timeshighereducation.co.uk/comment/opinion/they-has-arrived-at-the-pronoun-party/2017278.article#.VIHr5bJE0lk.facebook
- cassolotl, "Nonbinary Stats 2015 (worldwide) - the results." February 20, 2015. http://cassolotl.tumblr.com/post/111585517125
- cassolotl (Nonbinary Stats), "NB/GQ Survey 2016 - the worldwide results." March 2016. http://gendercensus.tumblr.com/post/141311159050/nbgq-survey-2016-the-worldwide-results
- Gender Census, "NB/GQ Survey 2017 - the worldwide results." May 2017. http://gendercensus.tumblr.com/post/160656902130/nbgq-survey-2017-the-worldwide-results