Alfred Carleton Gilbert was the largest U.S. toy maker in 1946 when it introduced the "American Flyer®" brand name. At the time the company was better known for its Erector Set as well as its chemical sets.
There is a brief, 5-minute video on YouTube of the A.C. Gilbert factory. If you really want to learn about the A.C. Gilbert history, we recommend sitting down with a cup of coffee or tea and enjoy Tom Barker's professionally-produced A.C. Gilbert Documentary.
A.C. Gilbert's main competitor was Lionel®. Gilbert wanted to make cheaper, and more accurate models. The main difference, beside the size (1:48 vs. 1:64), was that Lionel used a center rail down the middle of the tracks, whereas Gilbert used the more prototypical two-rail system. The A.C. Gilbert company manufactured American Flyer trains until 1966, when the company went out of business. Lionel then bought the American Flyer name and product line in 1967. Lionel subsequently declared its own bankruptcy later that same year.
The cereal company, General Mills, bought the Lionel product line, but not the corporation itself. In 1979 General Mills, under the name Fundimensions Division, based in Mt. Clemens, Michigan, resurrected the American Flyer product line, with little success. You can identify these models by looking at the label underneath, which will state "Lionel/Fundimensions". In the meantime "Lionel Corporation" continued as a holding company for a variety of toy stores around the country and wasn't really involved in toy trains anymore. In 1993 they went out of business for good.
In 1986 Lionel, LLC, owned by Richard Kughn, an entirely different corporation from the original Lionel company, bought the brand name and product line from General Mills. In 1994 famous musician, and part owner, Neil Young invented and holds some patents related to Lionel's TMCC system (digital command control). In 1995 Richard Kughn sold his interest to Wellspring Capital Management (80%) and Neil Young (20%, up through 2008). This is the Lionel company that is still in business today. Lionel's main business is O-scale trains, but they are now also actively producing both re-issues and newly-tooled engines, cars, and accessories under the American Flyer name. Their products are backward-compatible with original American Flyer track, but they are also starting to make some of their models more true-to-scale.
Jim Boyd (source: Railroad Model Craftsman magazine, October 1978 issue, page 76)
Malcolm Furlow (source: Railroad Model Craftsman magazine, September 1978 issue, page 102)
Buster Keaton (source: Trains Magazine web site)
Allen McClelland (source: Railroad Model Craftsman magazine, March 1977 issue, page 44; shows photo of his S-scale layout)
Mike Schafer (source: Railroad Model Craftsman magazine, August 2015, page 78)
George Selios (source: Model Railroader magazine, various issues)