Handwritten catalog cards became easier to read when typewriters were invented and in common use.
A lot of library systems turned to book catalogs in the 1970s. This allowed patrons to see all the titles owned by every branch in the system, but didn't tell them which ones were owned by the branch they were using.
In 1977, microfiche catalogs began to be used. The Library of Congress distributed them to certain libraries, then more libraries began putting their own catalogs on microfiche. Those were difficult to used because of the individual microfiche sheets and were usually only used by librarians.
By the early 1980s, libraries used microfilm catalogues. They had the same problem as the book catalog and the microfiche catalog in that it only listed all the books in the library system, with no indication which branch owned it or whether it was checked in or out. They were easy to use by the public - especially by pre-teen and teen boys who would sit side by side racing their microfilm catalogues to see who could reach the end of the film first - thereby ripping the film off the controlling roller and causing the whole machine to be unusable until we could fix it.
In the mid 1980s the first computerized catalogues entered the libraries. At first it was sold to libraries to help with clerical chores/ checking books in and out, etc. But the librarians immediately demanded these be on the Reference desk as well.
It was much more useful because it could also tell you 1) if the book was in or checked out of the library you were using and 2) if a copy of the book you wanted was owned by another branch library. Plus you could reserve it and it would be sent to the branch you used. Or you could call that other library and the librarians would hold it for you to pick up from there.
At first, computer catalogs were very slow - 900 baud. Then they jumped to 2400 baud and seemed so fast. The speed kept advancing and by the mid 1990s those same computer catalogs could also access the Wide World Web (Internet) and anyone could use the library's computers to search for anything.
That's where the catalogue is now.
What happened to the card catalogs? Most libraries kept using card catalogs as a double check. Finally, in the 1990s (or later in libraries that computerized later) we had a ceremony where we dumped all the catalog cards on the floor - then used them as scrap cards. It took years before we ran out of those old catalog cards.