From Wikipedia:
Involvement in the hobby can range from the possession of a train set to spending many hours and large sums of money on a large and exactingly executed model of a railroad and the scenery through which it passes, called a "layout". Hobbyists, called "model railroaders" or "railway modelers", may even maintain models large enough to ride (see Live steam, Ridable miniature railway and Backyard railroad). Railway modelers may find enjoyment in collecting model trains, building a miniature landscape for the trains to pass through, or operating their own railroad, albeit in miniature.
Some older scale models reach very high prices.
Layouts vary from the very stylistic (sometimes just a simple circle or oval of track) to the "absolutely realistic", where real places are modeled to scale. One of the largest of these is in the Pendon Museum in Oxfordshire, UK, where an EM gauge (same 1:76.2 scale as 00 but with a more accurate track gauge) model of the Vale of White Horse as it appeared in the 1930s is under construction. The museum also houses one of the earliest scenic models ever made - the 'Madder Valley' layout built by John Ahern. This latter layout was built in the late 1930s to late 1950s and brought in the era of realistic modeling, receiving coverage on both sides of the North Atlantic in the magazines Model Railway News and Model Railroader during the 1940s and 50s. Bekonscot in Buckinghamshire is the oldest model village, and also includes a model railway, dating from the 1930s onward. The world's largest model railroad track in H0 scale is Miniatur Wunderland in Hamburg, Germany. The largest live steam layout, with over 25 miles (40 km) of trackage is Train Mountain in Chiloquin, Oregon, USA.
Model railroad clubs exist where model railway enthusiasts meet. Clubs sometimes put on displays of models for the general public. One rather specialist branch of railway modelers concentrates on larger scales and gauges, most commonly using track gauges from 3.5 to 7.5 inches. Models in these scales are usually hand-built and are powered by live steam, or diesel-hydraulic, and the engines are often powerful enough to haul even dozens of full-scale human passengers. Often model railways of this size are called miniature railways. List of model railroad clubs.
One particularly famous model railway club is the Tech Model Railroad Club (TMRC) at MIT, which in the 1950s pioneered the automatic control of track-switching amongst hobbyists by using advanced technology for the time — telephone relays.
The oldest known society is The Model Railway Club (established in 1910), based near Kings Cross, London, UK. As well as building model railways, they also have a library of in excess of 5000 books, periodicals, etc. Similarly, The Historical Model Railway Society is a Society with its Centre of Excellence at Butterley, near Ripley, Derbyshire. It specializes in Historical railway matters and has considerable archives available to members and non-members alike.