The Church of Satan is a corporate body rather than an initiatory order. It is governed by a Council of Nine; LaVey was High Priest until his death in 1997, and Peter Gilmore has held the office since 2001. Local groups are called grottos. There are five degrees of recognition, and their conferral has been criticised, including by those who left over it, as having become honorific and purchasable rather than earned.
Membership is by paid registration rather than by initiation, and the Church does not publish audited figures. Its own implied numbers have run large. The best-sourced statement available is a newspaper report that membership was never above about three hundred, and any figure in the tens or hundreds of thousands should be treated as promotional.
The Church rejects the legitimacy of every other organisation calling itself Satanist. It lost Michael Aquino and others in 1975, who founded the Temple of Set on the ground that LaVey's materialism led nowhere and that the adversary was real. It has been in continuous public conflict with The Satanic Temple since that body appeared, characterising it as an activist campaign masquerading as a religion.
The 1980s brought the Satanic Panic, a documented moral panic in which allegations of organised ritual abuse of children circulated through police forces, therapists and broadcast media. Investigation found no evidence of the conspiracy alleged, the analysis published by an FBI investigator in 1992 remains the standard reference, but the panic ruined careers and imprisoned people, and the Church of Satan, which had nothing whatever to do with any of it, spent a decade as the popular image of what was being alleged.