Not on a lot of people's (well, Americans at least) radar, but Taiwan is both a super great country and has some cool train features for such a small island. High speed rail that runs on the west coast, higher speed lines on the east coast and some old scenic lines. The Pingxi line near Taipei is an old coal line that has been converted for tourism. Goes through old mining towns, right down the middle. The tracks are essentially the "Main Street" of the villages. Shifen is a popular destination on that line, where there are waterfalls nearby. My favorite is the Alishan Forest Railway that goes up to the Alishan National Scenic Area. It is an old logging railroad built over a century ago by the Japanese when they controlled the island. It is narrow gauge and has lots of winding turns and switchbacks as it rises from 30 meters altitude where it starts in Chiayi to Alishan at over 2,200 meters. A couple of smaller branch lines take five-minute rides within the park as well, and one of those lines has an extended early morning trip to a farther out spot for sunrise viewing. Another line is out of service and has been converted into a trail, but the tracks are still there as there is talk of reopening it.
There is also a cruise train that goes around the whole island in 13 hours. It's Disney themed, not to everyone's taste in that regard.
Taiwan, Taiwan: I could talk about it for hours. I called it home from 1990 to 2007, although there was a 3 year hole in the middle for me not working there, but my family remained there. First 5 years on the Taipei MRT, the last 9 years on the Taiwan HSR, from line on a map to riding the trains. With the exception of one 3 km segment, managed to ride the entire railway system. The round the island train did not exist while I was there. In fact, the south end link making a round the island trip possible was built while I was there. The trains, etc. on the HSR are Shinkansen. When the structures were started, the equipment and operating basics were supposed to be some form of combination of French and German. The Europeans were ultimately invited to go away, and I will skip the why, to be replaced by the Shinkansen system trains, power, everything operational. Shinkansen trains were far and away the better choice, since they are single level, near car floor level platforms, so much faster unloading and loading. (Is this a non-problem in Europe?) 3&2 seating in coaches, with a premium car, forgot what they call it, having slightly wider 2&2 seating. I never had any problems fitting my 220 pound body into the seats in the 3&2 cars. (The platforms meet US ADA (American with Disabilities Act) horizontal gap and are just a few mm lower than the ADA vertical difference.) Speed is 300 km/hr (186 mph), excluding short distances at each end and all concrete base track, excepting about 2 km on the south end. Track gauge 1435 mm. (4 feet 8 1/2 inches). The remainder of the railway system is 1067 mm gauge (3 feet 6 inches), except the Alishan Railway which is 762 mm (2 feet 6 inches) track gauge. The West Side mains and the East Side mains (to at least Hualien. I do not know about south thereof) are double track and electrified 25kV 60Hz with speed limit of 130 km/hr (81 mph). The top trains are EMU's. At the time I was there, there were four classes of trains with the lower classes locomotive hauled, and the bottom level unairconditioned locals. All levels were reasonably comfortable. Nice seats, but no dining cars nor compartments in any class. When I was there, all but the bottom were reserved seat trains, but they would sell tickets beyond the seating capacity with the understanding that you would be standing unless there was an unoccupied seat. There was a limit, but I do not know what it was.
The terrain is quite rugged, particularly on the east side. The roughly 80 km between Suao and Hualien was not built until around 1980. Before that to get to the southeast part of the island from Taipei was either by boat or driving on a one to one and one half lane road best described as a fingernail scratch on the side of a cliff. (This road is now a reasonably good two lane highway.) When we were there the railroad was single track with multiple tunnels, but has been double tracked and electrified since. I think much of the second main in the more rugged sections is on a somewhat offset alignment with semi-parallel tunnels. Not on the railway, but a fascinating sight is Taroka Gorge which is not far from Hualien. The drive up through the gorge is best described as like seeing the Grand Canyon from the bottom. The road is now reasonably good and has quite a few tunnels so some of the gorge sights can no longer be seen from the road. When we were there, the road was another fingernail scratch on the side of a cliff. Much of this is still open only for walking and maybe bicycles.
A side note: The Taipei MRT, which was why I was there for the first 5 years, is the first urban transit system in Asia that meets all requirements of the US ADA. Everybody involved was quite proud of that. A major part of the first line built, the Tanshui line is on the alignment of what was a railway branch line to Tanshui from Taipei.