Triturus and its relatives (Ichthyosaura/Mesotriton, Lissotriton, and Ommatotriton) are a diverse and widespread group of newts. While mainly European, several species can be found in the Near and Middle East. Calotriton (formerly Euproctus), the brook newts, are confined to Corsica and Sardinia.
The first salamanders described, this diverse genus of species and subspecies can be found throughout Europe and the Near-East. They are the animals that first come to mind when most people hear the word "salamander".
This group of Far Eastern salamanders are becoming increasingly popular in captivity, and thanks to the captive breeding efforts of one European hobbyist in particular (you know who I mean), they are becoming easier and easier to acquire.
The Tiger Salamanders and the Axolotl are so popular amongst hobbyists that they have been given their own topic. If you're particularly interested in the Axolotl, there is a large section of the forum devoted mainly to beginner Axolotl enthusiasts (not this topic).