I saw these on some car show. The brake discs are located just to either side of the differential as opposed to being mounted at the end of the axles with the wheels attached to them.
Was Jaguar the only manufacturer to use them? Does Jaguar still use them?
What are the advantages/disadvantages?
The Rover TC 2000 sedan had them. I don’t know what the advantages are supposed to be, although thinking about it, they reduce the unsprung weight, which improves handling.
I’m no engineer, nor a mechanic, but wouldn’t that tend to cause more wear on the axles in general and the CV joints in particular? Or maybe that would be a concern only for front-wheel drive cars?
That’s not even beginning to consider the inconvenience and cost of replacing the brake components. There’s also heat considerations…mark those up as some serious disadvantages.
Some Alfa Romeos too. And I believe some older Citroens like the Ami/DS/GS series.
In the case of the Alfas, it was for unsprung weight reduction. But I am not sure about the Citroens. It could be just some French engineering quirk. 
Right after I posted this, I watched “Classic Car Restoration” on DIY. It was an older show that featured a 1968 Alfa Spyder. They had the car on a lift installing the exhaust system and I noticed it had inboard brakes. It didn’t seem to be too difficult to get to the brakes.
One of the “historic” race cars that participated in a support race at Champ Car’s Long Beach Grand Prix had inboard brakes (at least at the rear). I got some nice close-up photos of them at the inside display/paddock area, but they’re on another machine and I can’t get to them right now.
I can’t recall which car it was, or even what type of car (I believe there were several F1, F5000, and a few other types tossed in), but apparently they’ve been tried in racing applications.
I think the reduction in unsprung weight is normally tossed out as the chief advantage. I also seem to remember hearing that cooling inboard brakes is something of a problem.
Wouldn’t there be a problem with dirt and debris?
They seem to be more exposed to the elements than conventional brakes.
Changing brake pads is easy. But changing the disk (rotor) is the hard part.