QAnon began in October 2017, when a pseudonymous user of the online message board 4chan started writing cryptic posts under the name Q Clearance Patriot. The person claimed to be a high-ranking official privy to top-secret information from Mr. Trump’s inner circle. Over two years and more than 3,500 posts, Q — whose identity has never been determined — has unspooled a sprawling conspiracy narrative that claims, among other things, that Mr. Trump was recruited by the military to run for office in order to break up a global cabal of pedophiles, and that Special Counsel Robert S. Mueller III’s investigation would end with prominent Democrats being imprisoned at Guantánamo Bay.

The anonymous posts subsequently moved to 8chan, where they remained until August, when that site was taken offline after the El Paso mass shooting. They now live on 8kun, a new website built by 8chan’s owner.

Some QAnon fans are hardened conspiracy buffs who previously believed other fringe theories, such as the bogus claim that the Sept. 11 terrorist attacks were an “inside job.” But many QAnon adherents are everyday Americans who have found in Q’s messages a source of partisan energy, affirmation of their suspicions about powerful institutions or a feeling of having special knowledge. Some are older adults who discovered the theory through partisan Facebook groups or Twitter threads, and were drawn in by the movement’s promises of inside information from the White House (some QAnon devotees even believe that Mr. Trump posts himself, under the code name “Q+”). Others are seduced by the movement’s wild, often violent fantasies, including claims that Hollywood celebrities are part of a satanic child-trafficking ring.

In online chat rooms, Facebook groups and Twitter threads, QAnon followers discuss the hidden messages and symbols they believe to be exposed in Q’s posts, or “drops” — for example, because Q is the 17th letter of the alphabet, a reference by Mr. Trump to the number 17 is seen as a possible signal of his support for them.

They watch “Patriots’ Soapbox,” a YouTube call-in show devoted to coverage of QAnon, and other niche media projects that have popped up to fill the demand for Q-related content. Reddit barred a cluster of QAnon groups from its platform in 2018, after a spate of violent threats from members, and Apple pulled a popular QAnon app from its app store. But other social platforms, including Facebook, Twitter and YouTube, still host large amounts of QAnon content. In general, these platforms do not prohibit conspiracy theories unless their adherents break other rules, such as policies against hate speech or targeted harassment.

The frequent introduction of new symbols and arcane plot points to dissect and decipher has given QAnon the feel of a theological study group, or a massive multiplayer online game. In interviews, several adherents described QAnon as a “lifestyle” or a “religion,” and said it had become their primary source of political news and analysis.