Early on all libraries were non-circulating libraries, and cards identifying users were unnecessary. With the public library movement in the 19th century, it became necessary to register users who were permitted to borrow books. Initially this was done with cumbersome ledger systems, with each page representing a borrower and the books borrowed (and returned) listed.
According to Helen Thornton Geer, in her book, Charging Systems (Chicago: ALA, 1955), in about 1900, John Cotton Dana, then director of the Newark (N.J.) Public Library, devised a system using a borrower's card and a book card. These early borrower's cards were not the simple identification cards of today, but rather a card with space to enter the date borrowed, date due, and date returned for each book circulated. As such they did fill up and the "Detroit system" of an identity card was developed by Ralph Ulveling in 1929.
In 1932, Gaylord Brothers introduced an electrically operated book-charging machine, using the basic two-card system devised by Dana. This system used a borrower card with a metal plate with an embossed number to register the borrower's identity onto the book card, which was filed by call number.
Through the following decades, various other machine-assisted and automated systems were developed, and circulation systems are now a key part of integrated library systems (ILS)--Geer's book, cited above, is a guide to the advantages and disadvantages of the systems in use in 1955. The metal plate has been replaced with a bar code in modern systems.
Older systems, some of which are illustrated in the links below, assigned each borrower a number which remained on the book card kept in the library book. With modern circulation systems, the borrower number is recorded only in the circulation system itself, and is disconnected from the book record once the book (or other library item) is returned, thus enabling compliance with ALA's Policy on Confidentiality of Library Records.