As there are over 12,000 current Android models from hundreds of manufacturers. There’s no way to include each and every one on a single page.
Some of these phones come with a method (either apporved by the manufacturer or found by a third-party) to unlock the bootloader and use the custom recovery method to root them. Many of these other phones can be rooted with applications like Kingo Root, with or without access to a computer. Phones from names you know, like Sony or Hauwei, are supported as well as phones from companies you might not have heard of like Vivo or Phicomm. You’ll find a partial list of supported phones here.
Apps like Kingo Root work because they take advantage of an exploit (a bug or glitch) in the software. This means that many security applications will identify them as a virus, and that software updates can (and do) break compatibility with them. Not every phone can be rooted through an app that leverage an exploit, but many can. It’s certainly worth a look to see if your particular phone is supported. These services are profitable, and profitability means time and money is spent to keep them current and working on as many models as possible.