SLT cameras are made by Sony as a kind of hybrid of the regular digital SLR design and the always-on live view of a mirrorless camera. They do have a mirror in the body, but it doesn’t flip up and down when you fire the shutter. Instead, it has a translucent surface so that the image can pass straight through to the sensor on the back of the camera.
The point of this design is that the fixed mirror can reflect light back on to the camera’s fast phase-detection autofocus sensor even while the image is being composed using a live view image on the rear screen or in the electronic viewfinder. The downside is that you get all the bulk of a DSLR without the clarity of an optical viewfinder. Sony still makes its SLT models but with improvements in sensor-based hybrid autofocus technology, most expect it will soon transfer all its efforts to its mirrorless models.