Mirror lenses are much cheaper to make and most optical manufacturer made at least one design. Canon, Nikon, Pentax, Minolta, Zeiss, and of course the Russians. But the most popular (cheaper) ones were made by third party lens makers, like Sigma, Vivitar, Tamron, and a plethora of rebadged brands like Makinon, Quantaray, and many others. Typical focal length ranges from 250mm Minolta RF Rokkor-X to the monstrous 5200mm made by Canon.
There are severe limitations to the mirror lens design. Other than the already mentioned small maximum aperture, the other is that the aperture is fixed. Furthermore, image quality is not comparable to the traditional glass lenses and for this reason, many people viewed mirror lenses are a cheap alternative to the real thing and wouldn't even consider using one, however cheap they were. Lastly, all but one mirror lens can auto focus, and that's the Minolta (Sony) AF 500mm f8.
One of the reasons people turned away from mirror lenses is the very dark viewfinder they see when the mirror lens is attached to the camera. Remember that all film cameras had optical viewfinders; the smaller the maximum aperture the darker the viewfinder becomes. If you ever tried a 500mm f8 mirror lens on a camera with optical viewfinder, you will see why; it's next to impossible to focus with such a dark viewfinder. Split screens do not work if the aperture is f5.6 or smaller. But dark viewfinder is just one of the inconveniences. The other, more severe shortcoming is the slow shutter speed caused by the small aperture and the need for faster shutter speed to counteract the shake due to long focal length. Most people shot ISO 100 to 200 film, and 400 is pushing it unless you are shooting black and white. So, that 500mm f8 mirror lens is pretty much limited to sunny days and mostly tripod bound, or you will get blurry pictures caused by mis-focus and/or too slow a shutter speed. As an example, for a 500mm f8 lens, you would need about 1/500s on full frame to ensure the picture is reasonably sharp, but on a cloudy or overcast day, you would have to crank up the ISO to 3200 in most some situations to attain the 1/500s shutter speed. For film, ISO 1600 is already hard to find and expensive, and the grain is the size of a golf ball. If you have never seen what picture looks like with the ISO 1600 film, you are just spoiled by the modern CMOS image sensor's high ISO capabilities :)
There are some very fine mirror lenses and three of them come to mind: Minolta AF 500mm f8, the Carl Zeiss Mirortar 500mm f8, and the Russian Rubinar 300mm f4.5, possibly the brightest mirror lens made for 35mm format. All of these lenses are very pricy or difficult to find. Fortunately, there are some gems amount the third party mirror lenses. I briefly looked at the Makinon 300mm f5.6, which is actually quite a nice lens. I am sure there are many more out there. My advice is not to let the name on the lens sway you. Try it for yourself. Often the noname lens was made by the same manufacturer as a more expensive lens with a different name.
Lamp Post - Sony A7 & Quantaray 500mm f8 Mirror Lens.