Xfce is the oldest of the popular lightweight Linux desktop environments. It uses the GTK+ toolkit, just like the more popular GNOME interface that serves as the default for Ubuntu and Fedora.
MATE is a fork of GNOME 2 that formed when GNOME was transitioning to version 3.0. If you’ve ever used a version of GNOME from before 2011, then you’ve essentially used MATE. Although some things have changed, the fundamentals remain the same.
LXDE uses the now very dated GTK+ 2 library, so the lead developer decided to switch to Qt instead. He combined his efforts with the RazorQt team to create LXQt in order to replace LXDE.